I like to start with a summing-up sentence, but I'm torn between emphasizing "because they couldn't" and "well, they did".

To start with, eighteenth-century monarchs and their families did not stay put in their capital cities/main seats of power year-round. Historically, European royal families went "on progress" around their realms, staying with local nobility and bringing the court with them: this both gave them access to regions that might need their attention (say there was a tendency for the area to have regular rebellions) and let them drain the coffers of problematic aristocrats. By this period, they were generally settled in their own properties - but that didn't mean they didn't move.

In France, the monarch held Versailles, of course, but also the Château de Marly (also built by Louis XIV), the medieval château de Saint-Germain, the château de Saint-Cloud, the château de Fontainebleau, and the Grand and Petit Trianons, as well as others. Louis XIV would regularly take the court to Marly to the end of his life, or rather, take some of the court: just as many of the traditions and ceremonies of Versailles were arranged to make courtiers compete with each other for shows of favor, the limitations on who could go to Marly created a new competition for the French aristocracy. Life there was more casual, though still otherwise much the same as at Versailles. He would take the entire court to Fontainebleau and a chateau at Compiègne for a few months twice a year, the former in the fall and the latter in the spring. He also had the Grand Trianon built near Versailles at the end of the seventeenth century, and would use it as a place for evening entertainments or summer hangouts for the whole court, but didn't really live there. Louis XV would build the Petit Trianon, more of a country house than a palace, on the grounds for his mistresses en titre to live in; Marie Antoinette later used it as her personal getaway with an extremely exclusive circle. In the 1780s, Louis XVI bought Saint-Cloud as a retreat along the same lines as Marly (which by this point had long been out of use) - a place that was somewhat more casual and also supposedly more healthy for the children.

The English monarchs had the more official St. James's Palace, but also Kew Palace, Windsor Castle, Kensington Palace, and Hampton Court Palace. St. James's was like Versailles - the official home of the court, where official ceremonies took place (like the Drawing Rooms where people were presented to the sovereign). Georges I and II tended to also use Hampton Court Palace and Kensington Palace, which had been traditional "side palaces" of the last few generations of English royalty, where they would rule from in a slightly more casual setting, and where they tended to go when ill and/or dying for comfort. George III, on the other hand, wanted more privacy and security than was possible at St. James, and so bought Buckingham House (later remodeled into Buckingham Palace) for his family to live in during "the Season", when Parliament was in session; they lived at Kew Palace or Windsor Palace, outside the city, in the summer. This is when Kensington would transition into a home for royal offspring, like the Duke and Duchess of Kent: Queen Victoria would live there until her accession.

(Other monarchs had similar setups, but I'm most familiar with England/Great Britain and France.)

This represents quite a lot of traveling per year, particularly when we're talking about full court moves. When the French court went to Fontainebleau, that means all the courtiers, all the servants, all the cooks and pages and guards and tailors - it's a massive logistical problem and expense, and then it had to be done when they came back! Likewise, moving from Buckingham House to Windsor was a big undertaking. Going farther afield in a more touristy, modern vacation would compound the difficulty and expense.

However, the thing that all of these palaces have in common is that they're not really that far from the seat of government. Versailles, Marly, and the Trianons are all practically right next to each other in the southwest of Paris, while Fontainebleau is just in the southeast, and Compeigne is a little farther outside of Paris to the north. St. James's Palace is practically next door to Buckingham House and about a mile away from Kensington Palace, while Kew is in Richmond, now a part of western London, as is Hampton Court in Molesey; Windsor Castle is actually outside of London, in the country, which is why it worked for a place to live outside of the Season. While monarchs of this period were no longer quite as absolute as they had been in earlier centuries, they were still central to the ruling of the kingdom, and they couldn't completely disappear for weeks on end. The best solution was to have nearby spaces where they could relax in the short term.