Does Boston simply have an extremely high proportion of Irish Americans?

Yes, historically Boston was a site of major Irish immigration, beginning as early as the beginning of the 1800s but massively increasing from 1840-1870 as the influence of the Great Famine was felt in Ireland.

In the earliest decades of the nineteenth century, the general contours of Irish immigration was to first stop off in the ports of Atlantic Canada (Halifax, Montreal, Quebec) because the shipping rates to those ports were cheapest^1. After a few years, they would then move south to American cities such as Boston, New York, and Philadelphia. In this period from 1800-1820, the majority of immigrants from Ireland tended to be Irish Protestants, owing to the fact that Protestants tended to have greater resources to manage the trip across the atlantic.

In the period from 1820-1840, the demographics and contours changed, with greater numbers of impoverished Catholics leaving Ireland and heading directly for Boston or New York. This immigration of Catholics did prompt hostility from a Protestant Yankee native population, and this period saw some notable anti-Catholic riots. The most notable event in Boston was the burning of the Ursuline convent in 1834. Another famous confrontation was the broad street riot in 1837.

As the Great Famine ravaged Ireland from 1845 to 1849, massive numbers of Irish people left the island, far greater in scale than previous migrations. 200,000 Irish immigrated to America in the decade of the 1830s. In the 1840s, 780,000 Irish came to America, mostly after 1846. At the outset of the Famine, Boston had a population of approximately 115,000 residents. In 1847, the first year of major migration due to the famine, 37,000 Irish arrived in Boston^2.

Like the earlier immigration from 1820-1840, this influx of Irish Catholics into a Protestant Yankee majority led to anti-immigrant hostility in the 1850s. In that decade, Know-Nothing politicians filled the State Senate, State House of Representatives, served as Governor and as Mayor of Boston^3.

As others have said in this thread, migration tended to flow towards established communities of Irish-Americans, where a migrant might have family or friends already living there. Thus, in the post-Famine period, Boston continued to see heavy migration of Irish people into the 1870s, and lower levels of migration into the 20th century.

and why Boston, as opposed to any other major American city?

As I said above, other cities like New York, Philadelphia, Savanna and New Orleans all saw migrations of Irish into their cities in the 1840s and 1850s. The immigrant vote was quite important to the functioning of New York's Tammany Hall political machine in the later decades of the 1800s. Additionally, New York City saw severe Draft Riots in 1863, and newly naturalized Irish-Americans played a large part in these riots. They were partly motivated by resentment of exemption provisions, when working-class immigrants could never afford to pay the $300 required. Partially too, the Irish and German immigrant workers were driven by fears that abolition of slavery would result in labor competition from free Blacks.

In any case, New York City did not become as closely tied to Irish identity as Boston did for a variety of reasons. In the late 1840s and 1850s, New York saw German immigration at the same time and in similar numbers to Irish immigrants. Also, New York has hosted subsequent waves of Italian, Jewish, Balkan, Chinese, and other ethnicities, which made the city a patchwork and prevented New York from being associated with any one community. Boston, in contrast, did witness large Italian immigration into the North End, but not a similar scale and variety of immigration as New York did.

Of course, cities like Philadelphia and Chicago continue to have notable Irish-American communities, and noteworthy St Patrick's day parades.

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1. Enclyopedia of American Immigration pp 154.

2)http://www.historyplace.com/worldhistory/famine/america.htm

3)Hidden History of the Boston Irish pp 21