There's a small and extremely simple-looking place in Trastevere, Da Enzo, that is a target of some of the foodie walking tours and is said to be popular with off-duty chefs. It specializes in local dishes. Do not expect fancy surroundings, and do make a reservation. I enjoyed an early lunch there one day and would have liked to return but no reservation meant no table. I'd call the food "rustic" rather than "refined", but it is good. I see squash blossoms on the online menu, so it seems that they update it seasonally.
The need for reservations in Italy has come up a few times here. You will benefit greatly by calling ahead or stopping in at lunchtime to make a dinner reservation. As has been explained by knowledgeable travelers, Italian restaurants typically do not schedule multiple seatings, so if there's a reservation for 9 or 9:30 PM, the table will not be available to you at 7 or 7:30.