We very much liked staying at this airbnb apartment: CA'GIRASOLE WITH WI-FI ---- https://www.airbnb.com/rooms/1325679?guests=1&adults=1
It's right off the Via Garibaldi in the area called Castello ---- a few yards away from the Grand Canal, very untouristy, very neighborhoody, right between two vaporetto stops, beautiful view from the Via Garibaldi across the Grand Canal, and lots of nice places to eat. 10 minute walk along the Grand Canal to San Marco, so it is impossible to get lost. The apartment has no views at all and a rather small kitchen, but the host is pleasant and is was less than $75 a night. It's almost as far from the train station as you can get, if that matters to you --- we liked it that it was.
A vaporetto pass (purchased from outside the train station) is worth every penny because then you can treat the vaporetti like a hop-on/hop-off bus and get anywhere you want to get to or just ride it for fun.