Venice in 48 Hours, On a Budget!

hi,

my boyfriend and I will be in Venice from 7-9th June for two days and want to stay somewhere moderately nice, but still affordable! Our budget is $100 per night, tops. We would like to stay in Venice itself, and of course would like a good location, though not necessarily super touristy! We are going to be traveling with others, and wouldn't mind staying at an apartment, but will any one give us an apartment for only two days?

Any suggestions would be most welcome. Thanks!