We had no expectations of having any good meals when we were in Venice last Christmas. In fact, one actually needs to reduce their standards even lower the closer they get to St Marks. Finally, if you are anywhere near the main routes from the train station to St Marks, you're probably better off grabbing Mickey Ds.
That being said, we actually did score a fantastic lunch one day in the back streets near the hospital (Scuola Grande di San Marco). My wife and I are determined diners, and we'll often defer eating while we tirelessly march around checking out various restaurants. On this day, we were nearing our capitulation point when I noticed a tradesmen down a small alley standing outside having a smoke. He had taken his glass of wine with him, and was then joined by a friend who looked like a local fisherman.
With my spidey senses tingling, I mosied down the alley to have a look. I asked the guys - in badly fractured Italian - if the food was any good. They seemed to understand, and gladly said yes, but thought it might be too late for lunch as it was small & crowded. Well, I pushed the door open to reveal a micro, tiny bar/restaurant that could seat under 20 people, with maybe 8-10 jammed into the bar.
I asked the hostess if they had any room, and she said wait outside for a few minutes to let her see. I went back out to tell my wife we scored if they had room. Shortly after, the hostess (as it turns out, the wife of the owner/chef), came to get us and squeeze us into a small table for 2.
The fisherman/plumber/contractor group was comprised of around 8 guys all drinking and having fun (it was Saturday afternoon after a short 1/2 day after work). There were some French tourists along with some Italians, but we were the only Americans. We ordered the sampler plate, including such staples as sepe al nero, bigołi in salsa, sarde in saor, etc. Basically, we went hog wild.
It was sort of fun playing tourist, taking photos of each plate, hanging out and having fun. Finally, we were the last diners as the lunch period had closed, and they needed to start prepping for dinner. The chef came out and we talked about some of the dishes. I ended up getting a great photo of him and my wife - I guess I can't post a photo here, but here's a link:
https://lh3.googleusercontent.com/LsG55zKtY7Quqcp7IAOcMRIyfirokgBSB4M99-dm7aDsivP3-kqoDE9kzfEhCo7w7Fr9wsOYctiq=w1600-h900-no
https://lh3.googleusercontent.com/zqnW0fU3fb8tjndxb7LvTfdXe5bFaOLrwF7LL3V5rehzATMbIK_IqFd0UeZpmAnIiy9QG1xwr97V=w1600-h900-no
https://lh3.googleusercontent.com/5MLDc3DeFLol_13pYZUHiayR4lirlQqfnimn2ugH6eA_HZV9Ltx8Go_jdUD4lrb14MZz45WQpVfk=w1600-h900-no
I won't mention the place by name, because it's tiny and will just get slammed even harder. It's just over the Calle Larga Giacinto Gallina - it currently has 4.5 stars on a number of different review sites. If you're in the area, you'll be able to find it.