Mercado San Miguel

try their web site: http://mercadodesanmiguel.es/
opening hours at the bottom of the page

And so Turistic to me...

but still yummy

I saw plenty of locals there, at least in September 2015. It's also a great option if you want food outside of sit down restaurant hours (there's a long gap between lunch and dinner at table service restaurants), or if you want a variety of foods in one place.

In short, I didn't find it so touristy, and touristy or not, I liked it a lot (went several times).

Ditto to what Harold said. I was there in late May 2015. It's certainly possible that the locals have started ignoring it in droves since then.

It’s always been busy when I’ve visited, so it must be doing something right.

I stopped by at about 10:30 in the morning, and it was lovely, not at all crowded. Unfortunately, I wasn’t really hungry after a good breakfast. Probably explains why it wasn’t busy.

We stumbled on this place, hadn't read about it and thought 'oh how charming'. And then we went in. Lots of luke warm overpriced tapa and watery drinks -- we hope the turnover is high because it looked really like great incubation temperatures -- the food we tried was not very good, although the desserts a bit better than the savory items. And the place was crawling with bus tours. We were so much happier on tapas crawls on streets with lots of bars like Cava Baja where locals were having drinks and tapas as well rather than what seemed like a tour group station with prices to match which was the Mercado San Miquel.

Maybe it depends on the time of year. I was there in February and there weren't any tour groups but there were both locals and tourists.