Seeking the wisdom of the Flist

I know that several (possibly many) of you have been to Venice. I'm planning a trip in June, and want to rent an apartment. I've got an offer of one right off St Marks Square - it's TINY, but the price is right and I like what reviewers have said about the landlady (and it's on the 2nd floor). However, just not sure whether just off St Marks Square would be really desirable or not... Any thoughts or ideas? If you were going to stay in Venice, especially if it were your first visit and potentially your once-in-a-lifetime chance to go, where would you choose to stay?