In case you're still looking...if it's for a shortish period of time and you can't get an apartment, we stayed at Dimora Serenissima (http://www.hostels.com/hosteldetails.php?HostelNumber=14446), which is sort of like an agency for rooms scattered around Santa Croce. We were given keys to a residential apartment block (very secure) with a large double room, very clean, with own fridge and bathroom. It wasn't too expensive (for Venice), though obviously depends on demand. I think Residenza Santa Croce (http://www.hostelworld.com/availability.php) are the same group.
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