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Venice Accomodation Reviews
Below are some places that usually get positive writeups--in various locations with various amenities in your parent's general price range (though this can be impacted by demand and events in Venice).

But here are some websites that you can check out. Some things to watch for--do you need an elevator? Do they want a room on a canal, or THE Grand Canal, or not? Is room size important to you?

note the eurocheapo web site I used for one of the hotels--it's a good site and doesn't list flop houses as the name might imply.

http://www.pensioneaccademia.it/

http://www.lacalcina.com/

http://www.locandaartdeco.com/

http://www.eurocheapo.com/venice/listings/selection/laresidenza.asp

http://www.sancassiano.it/

http://www.aironehotel.com/  

http://www.hotelbernardi.com/
Hotel Alex - http://www.hotelalexinvenice.com/

Hotel Alex is a great place to stay and Venice is a great place to visit
Ai Do Mori - http://www.hotelaidomori.com/en_hotel1.htm

My daughter and a friend went to Venice in the fall of '99 and stayed at the Ai Do Mori. They were quite comfortable and satisfied with it.
Hotel Alex - http://www.hotelalexinvenice.com/

We stayed in a double with shared facilities and never spend more than $50 per night.  
Ca' Venezia - http://www.bootsnall.com/hostels/eu/it/ven/1553.shtml

I stayed at Ca' Venezia in Venice. It's not really a hotel, they just have 7 studio's, with kitchen and bathroom. Very convenient if you want to save some money by cooking for yourself. There was often no hot water though. The location is perfect: a 5 minute walk from San Marco!
Ai Do Mori - http://www.hotelaidomori.com/en_hotel1.htm

Here's another possibility in Venice, Hotel Ai Do Mori. My daughter and a friend stayed here and recommended it.
mailto:gtsheep@hotmail.com
Hotel Giorgione - http://www.hotelgiorgione.com/

Hotel Giorgione(Venice) was a wonderful splurge for us in 2001.