Just remembering some decent meals from a couple years ago, so no guarantees these places are still good, but -

Osteria il Milion was a good lunch spot for us. It claims to be the oldest osteria in Venice - I can't verify that. They're pretty close to the Rialto bridge and have a menu in like 4 languages, so it's the kind of place I'd normally tell you to stay away from. I remember sitting outside, a pretty serviceable house red, and the sarde in saor being what I'd go back for.

We had dinner at Bistrot De Venise, which serves what they call "historic" recipes - basically food from Venice's past. We did tasting menus, one modern one historic, and really enjoyed it. EDIT: Bistrot De Venise is in the Michelin Guide (not starred, but written) for 2014.

Both of these places are located close enough to Piazza San Marco and Ponte Rialto to be tourist traps. Hell, maybe they were, but we had a nice time - certainly the two meals I remember from our last time in Venice. The rest of the time, I assure you, we ended up in actual tourist traps, complete with mediocre food. I didn't do my homework before that trip.

EDIT again: I forgot Trattoria alla Madonna. Also in the Michelin Guide as a Bib Gourmand. I walked into this place with a real sinking feeling, but it ended up being very good. It's in tourist central. We walked in, total shot in the dark, after asking some random person on the street who I heard speaking in the local dialect (which I cannot understand). It worked out well.