Hey, Ralph...
My last few trips to Venice were with a group and a significant budget, so I'm probably not the guy to ask about cheap Venetian eats (though there are plenty who would insist there's no such thing), but I did all of the restaurant planning for the upscale joints and here are some faves. This is all going back 2-5 years, so hopefully it isn't too out of date.
My personal favorite sweet spot in terms of cost vs. deliciousness was Fiaschetteria Toscana. Warm, cozy, good mix of tourists and locals, great meals and friendly staff. They do sort of a cleaner, dressed-up version of sarde in saor that uses sole instead of sardines, and I remember getting an incredible linguine al cartoccio one trip. Despite the name, it's mostly Venetian specialties that have been cleaned up and refined just a touch.
For something a little more cutting edge, Da Fiore is dynamite. Pricier, fancier, dark and dramatic, explosive food. Rooted in Venetian, but a little more freeform. This place has gotten a lot of press, and deservedly so. If you want to get a sense of the food, they've released a cookbook of the same name. They do a black risotto with lemon zest that just about made me weep.
If you really want to abuse your wallet, you can always hit Harry's Bar. It's kind of corny and commoditized, with the logo on your bellini glass, but the food really is fantastic. Dinner will make you weep. The bill will make you wail. Their fegato alla Veneziana is potentially my favorite liver dish anywhere. They slice it thin and cook it fast and hot to get just a little crisp on the edges... woo.
Considerably less abusive, though not exactly cheap is all'Angelo. We actually ended up falling into this place three times on our last trip, enjoying it a little more with every visit. Very friendly folks, considerably more casual than the others listed so far, fantastic food. Had another killer linguine al cartoccio here.
One anti-recommendation is Al Covo. This place gets tons and tons of press, and I'm absolutely mystefied as to why. Probably because it's a husband and wife team... the husband, Venetian, runs the kitchen while the wife, Texan, runs the house. People rave about the food, and I thought it was competent but unexciting. I think it's only exceptional in comparison to the marker board tourist traps that surround St. Marco, and the crowd did seem to be mostly comprised of Americans who didn't want to be challenged too much, so that may have something to do with it.
Hopefully that helps on the upper end of the spectrum, anyway.
Dominic Armato
Dining Critic
The Arizona Republic and
azcentral.com