I did a search, but all of the threads that came up were a few years old or more, so putting it out there for any post Covid experiences. Probably better to find something closer to the Uffizi in case service is very relaxed.
We are climbing the cupola in the morning, then have Uffizi tickets for 1:30, so need a nice lunch in between. We enjoy good food, but are not really foodies (gastronome). So local charm, enjoyable food at reasonable prices (ie, typical for the area for a nice quality meal — budget is not super tight). We will be there in early May, so maybe outdoor seating, or rooftop? Quaint indoor ambiance. Pretty flexible.