We might find ourselves at the Piazza at lunchtime, if we take advantage of using the Secret Itineraries tour and reserved tickets to the Basilica to avoid long lines, since the tours are only in the morning. It looks like most of the places near the Piazza are expensive tourist traps--any suggestions for someplace close by that isn't?
A little off topic, but wherever you decide to have lunch be sure to save room for the best gelato on the planet at Suso Gelatoteca. It's a ten-minute walk from San Marco, closer to the Rialto Bridge, but SO worth the steps.
Just walk to the northeast a short distance and you'll quickly be out of the high rent district. But keep this in mind, ALL eating places are touristy. A place that gets 20% of its business from locals would be positively a local hangout.
The RS Venice guide suggests the café at the Correr Museum. Anyone tried it?
We ate there on a visit last year. They serve sandwiches and salads and a side of fruit. It was good. I would eat there again. It was reasonable priced.
We went down the little street just beyond the Bridge of Signs that Rick refers to as "sandwich alley" or something and got sandwiches at one of the places her recommended. The service was friendly and the little shop where we stopped had air conditioning that actually worked. The food was ok and very expensive. We did not care much as we were starving and exhausted. I would suggest walking a little farther away from Piazza San Marco if you can. If not, the restaurant at the Museum is probably your best bet given the positive review above.
We enjoyed this restaurant, located just to the north of San Marco and even went back a second time. It is a chain and not a "local" place, but everyone in our group enjoyed it.
http://www.rossopomodoro.it/ristoranti/VENEZIA/centro-storico#
FYI, bakeries sell little sandwiches and bottled beverages for takeaway......