I would highly recommend Verona as a base for the Veneto - my favorite part of Italy, by the way. It's got all the things you are looking for, plus it's big enough to offer some diversity. It's a fairly sophisticated city so you should be able to find good markets, etc.

There are tourists, but few of them are from the USA. Lots of other Europeans however. And every evening the Veronese are out walking on the main streets of the old part of town, which is a pedestrian area. The train situation is good because Verona is on the east-west and north-south rail lines. There are also lots of interesting things to see in the area by car.

The French fries there are the best I've ever eaten - no, I'm not exactly a gourmet diner - and there is a pizzeria that we frequent that has the best pizza we've ever had in Italy.

Sorry I don't know anything about renting an apartment, but I may be able to find some info. about that.

Callie in New Orleans