Massachusetts:

As Jack N. Rakove explains in The Annotated U.S. Constitution and Declaration of Independence:

"In 1768 Governor Francis Bernard had moved the Massachusetts General Court from Boston to nearby Cambridge, and in 1774 Governor Thomas Gage convened the assembly even farther away, at Salem."

(Note: The "Massachusetts General Court" was the name for Massachusetts' colonial legislature.)

In American Scripture: Making the Declaration of Independence, author Pauline Maier argues that this grievance was one of the lesser grievances cited in the document. Cambridge was only four miles away from Boston, and the legislature had moved legislative sessions there before, during a smallpox outbreak in Boston.

However, as Donald C. Lord and Robert M. Calhoon recount at length in their article "The Removal of the Massachusetts General Court from Boston 1769-1772" published in The Journal of American History, the move under Bernard "provoked a constitutional crisis in Massachusetts and instigated a controversy which lasted for more than two years" and the General Court "suspected him of harassing the Court out of whimsy". They argue that Bernard recognized it as a "risky step", but one he took because he was "so disturbed by the erosion of royal authority in the province that he was determined to preserve one of the crown's prerogatives from further deterioration". The ploy was to get the Massachusetts General Court to meet outside the influence of the anti-royal, pro-revolutionary atmosphere in Boston. But ultimately, moving the Court to Cambridge made no difference. The Court was moved back to Boston after two years.

James Bowdoin, a pro-Patriot, anti-Royal, member of the Massachusetts Governor's Council, wrote gratefully upon the latter move:

"...the removal of ye General Assembly to Boston, as well as from it, has proved alike ineffectual to bring them to an acquiescence with ministerial measures. The air of Cambridge & of Boston is equally unsuitable..."

In 1774, British Parliament passed the Massachusetts Government Act which basically put Massachusetts under martial law. British Army General Thomas Gage was appointed the Governor of Massachusetts and the new law essentially gave him ultimate authority over the General Court, including dissolving it completely. He arrived in Boston on May 13. On May 25, he met with the General Court for the first time. He rejected all their nominees to the Governor's Council and essentially appointed his own. He dissolved the legislative session and ordered that it reconvene a week later in Salem, about 25 miles away. Again, this was an effort to get the Court outside the influence of the revolutionary spirit of Boston, which was exacerbated by the fact that Boston was now under military control, with British Army soldiers patrolling the city.

The Court didn't actually reconvene for two weeks, holding their first session in Salem on June 7. The Massachusetts Government Act also gave the Governor the power to forbid any legislature (including local ones) from meeting without the Governor's permission. Almost immediately, there were secret sessions being held by the General Court, without representatives of the Governor present, to discuss petitioning the other colonies to form a "continental congress" through which to respond to Britain's latest actions. Once Gage got word of the meetings, he sent men to break them up as illegal. In the end, the government only met officially in Salem for ten days. On June 17, Gage dissolved the government.

On September 1, Gage ordered a new election for the General Court, with the new session to begin in Salem on October 5. However, when the election did not favor the royalists, he discharged the newly elected representatives on September 28, before the scheduled session. The newly elected General Court met anyway. On October 7, they passed a resolution to style themselves the "Provincial Congress" and adjourned themselves. They reconvened on October 11, in Concord, opposing the authority of the royally-appointed Governor and Governor's Council.

South Carolina:

A parallel event happened in South Carolina, one that was more personal. As recounted at length by Alan D. Watson in his article "The Beaufort Removal and the Revolutionary Impulse in South Carolina" published in South Carolina Historical Magazine, the move of the colonial capital of South Carolina was instigated over a housing issue.

In 1769, the South Carolina legislature (called the House of Commons) had appropriated money "to support the cause of the London radical John Wilkes, viewed by many Americans as the 'unshaken colossus of Freedom' who dared to oppose the king in the cause of liberty". This came about because, for about two decades, the House of Commons had been allowed to appropriate funds directly from the treasury without the assent of the Governor or Governor's Council, even though they were supposed to assent. The result was that the Governor's Council started requiring their assent again. They then vetoed a tax passed by the House to repay the Wilkes Fund, leading to a standoff. And then the governor, Lord Charles Montagu, actually showed up for the first time in two years, to enforce the law, arriving in September 1771.

This event came to be known as the "Wilkes Fund Controversy". During the ensuing political standoff, when Montagu arrived in Charleston, he found he could not find a suitable house. Few houses large enough befitting a governor were on the market, and the House of Commons refused to pass legislation to fund his lodging, or to build a new one. As Watson explains:

"...the difficulty of housing the governor proved distracting not only to Montagu but to the citizenry of the Charleston area. Finding his choices for a private residence narrowed to a tavern, a public boarding house, and the military barracks of Fort Johnston, Montagu selected the last as most fitting for a governor of the colony. However, the decision necessitated a three-mile ride from James Island in the Charleston harbor on which the fort was situated to the town and a similar return trip each time the governor chose to visit Charleston. And Montagu demanded that the batteries of the fortifications along the way salute as he passed.

"The noisy salutation betokening the arrival and departure of the governor prompted the Commons to lodge an official complaint against the needless expenditure of powder. The wastefulness and disturbance also elicited critical comments in the press about the governor's extravagance and vanity..."

Before taking the lodging he did, a member of the Governor's Council had already written to Montagu to urge him to move the capital from Charleston to Beaufort, South Carolina, in order to render the House of Commons "more sensible of the great inconveniences arising from the want of a Governor's House at or near the Metropolis."

Watson writes that Montagu had initially been resistant to any such move, but with the anti-royal, pro-revolutionary sentiment growing in Charleston, he eventually changed course. On August 28, 1772, he dissolved the current session of the South Carolina House of Commons, called for new elections to take place on September 22 and 23, and called for the next session to convene on October 5, in Beaufort, about 70 miles south of Charleston.

As Watson explains, Montagu's reasons weren't just for the housing issue, though it did play a role in the instigation. It was also an effort by Montagu "to induce a measure of anxiety and distress among" the pro-revolutionary members of the House of Commons, mostly centered around Charleston, but also to rally support from members of the House who lived in the Beaufort area and support the royalist side.

Instead, the plan backfired. Nearly all the same members of the House were re-elected, only now they were more united than ever against the royalist government. One of the House's first orders of business at the new sessions was to form a "committee on grievances" to investigate the removal of the capital to Beaufort. Watson summarizes their findings:

"The committee determined that Montagu's calling an assembly to meet at an unusual site without access to public records, and at a time injurious to the public health and inconvenient for private affairs, justified an immediate cessation of legislative business until the governor had given satisfaction for his extraordinary behavior. Nevertheless, in light of the need to minister to public concerns, the committee instead offered three resolutions which condemned Montagu for his affront to the representatives of the freeholders of the colony, for an 'unwarrantable Abuse of a Royal Prerogative which hath never been questioned by the People of this Country,' and for his evasion if not violation of the provincial election law by proroguing [i.e., dissolving and calling a new election] the Assembly before it had an opportunity to conduct business."

Summary:

These were the two events that led to that grievance in the Declaration of Independence. While the move in Massachusetts of the capital from Boston to Cambridge a few miles away may be overstating the case that it was "unusual, uncomfortable, and distant", the move to Salem about 25 miles away was. And in South Carolina, the 70 mile move from Charleston to Beaufort was, too. Both were more than a day's travel, which justified the accusation it was "distant". And that distance meant that the entire assembly had to find new lodging, and for an unknown period of time since the governors made no indication if the moves were permanent, and how long they would last. Hence, they were "uncomfortable". And they were also "unusual" in that the capital in all three moves was eventually moved back. And also "unusual" in the sense that the new sites were chosen as capitals more for political purposes rather than practical ones.