Not sure exactly the type of food or price range you are looking for, but I can recommend the following:
Venice:
- I would check out the blog from Skye McAlpine at http://www.frommydiningtable.com/. She lives in Venice, recently published a cookbook on Venetian food and has a good selection of restaurant options at different price ranges in Venice.
- If you are looking for a special occasion restaurant with local and fresh Venetian food, I can highly recommend Al Covo: https://ristorantealcovo.com/. We went there for a birthday dinner at then end of May and the food is fantastic. Try the local catch of the day from the Adriatic and the veal in tuna sauce. The wine list includes good local options as well.
- Rose Salva: http://www.rosasalva.it/en/. This old fashion pastry and bakery shop near San Marco has a delicious assortment of fresh salads, pasta, and sandwiches. It has small amount of seating inside along with tables that you can stand and eat a bite. I would recommend the pesto pasta with a glass of vino.
- Rossopomodoro:http://www.rossopomodoro.it/ristoranti/VENEZIA/centro-storico. Near San Marco, this is excellent pizza. They specialize in a 24-hour slow rise, thin crust pizza with simple toppings. They also have delicious salads and specialities such as Branzino. I cannot believe that I am recommending Pizza in Venice, but my niece insisted on having Pizza. Since we have returned to the US, she refuses to eat Pizza here and we had to get the recipe for the crust and have a friend translate it from Italian, it was that memorable.
Florence:
- Not a restaurant, but a great introduction to the food of Florence/Tuscany is the Eating Italy Food Tour: https://www.eatingeurope.com/florence-food-tours/. We took the sunset tour and visited small local cheese shop, had the signature drinks of Florence, sampled Ribollita, and the famous Florentine steak. It was one of the best experiences we had eating in Florence.
- For a mid-price, authentic Florentine meal, I can recommend Trattoria Pandemonio: http://www.trattoriapandemonio.it/. We went there in early June for my other friend's birthday. They have all the traditional Florentine meals, plus some surprises, including a delicious eggplant flan and one of the best seafood risottos. This is a family owned place with a good mix of both locals and tourists.
Have a great trip.
Sandy