Hi Lynn,

Venice for the most part is very safe. Eventhough we stayed this summer in the San Marco area ( Hotel Metropole), there are other great areas a bit farther away from the hustle and bustle.

One hotel which is reasonable in price and very popular is Pensione La Calcina www.lacalcina.com It is located in the Dorsoduro area, facing the Guidecca Canal. I went by it several times and it looks lovely.
I couldn't get reservations there, it's so popular that it gets filled many months in advance.

We liked very much the Hotel Metropole. We went in August, which they consider the "low season" ( although Venice was mobbed by tourists!), so we got a decent rate. Their website is www.hotelmetropole.com

Good luck! Venice is very special!