] I always assumed JA chose Cambridge because of the Fitzwilliam connection there.

That hadn't occurred to me. See the link below, which indicates that the Museum was set up in 1816, after P&P, but we may presume that Fitzwilliam had some earlier connection with Cambridge.

Incidentally, this was a different Fitzwilliam from the Whig Earl.
http://www.compapp.dcu.ie/~humphrys/FamTree/Fitzwilliam/irish.7th.viscount.html
(I like the bit that the 7th Viscount abandoned the idea of leaving his money to the other Fitz because he was `appalled by the Earl Fitzwilliam's manners in drinking tea'

The 7th Viscount was the Cambridge Museum man, and the Whig magnate is referred to confusingly as either the fourth or the second (he was the fourth holder of the Irish earldom, and the second holder of the English earldom of the same name.)