Hey Clair:

Burlington is an awesome city on the lake.
Quite beautiful this time of year...
I would suggest staying somewhere overlooking the lake like the Courtyard Marriott.  It's actually nicer than the Hilton right next door, although both have lake views.
As far as dining goes, you cannot go wrong in Burlington...
There are a million great places fancy and casual.
On the fine dining side within walking distance from the hotel I would suggest L'Amate and Trattoria Delia.  If you like Italian, hit up Trattoria for sure.