Well, I don't know what you consider "near" as much of Florence is within walking distance of itself, but one of my favorite restaurants I keep going back to is Ristorante la Spada, about 300m from your hotel? haha I like to refer to it as the meat restaurant, I assume "the sword" is actually meaning the thing that they roast all the meat on :) But my dad loved his plate of meat, and I loved my pici senesi pepe e pecorino dish (like cacio e pepe from Rome, but different pasta and maybe other differences?) so much that I came back two nights later and had it again. Then 4 years later I was determined to go back to eat it again and they didn't have it on the menu! So I asked them and they enthusiastically agreed to make it for me and it was just as delicious as it was before! Good news, its back on the menu now :)
It might be super touristy, but I know that it was hoppin at all times when we went, and I would probably always go again.
https://www.ristorantelaspada.it/en/index.php
And touristy of all touristy, I make a point to always visit Trattoria ZaZa, its off the central market area. I ALWAYS get the pappardelle all chingiale with the filetto di pepe verde to share with people (then the crema di mascarpone that comes with strawberries!). I ALWAYS make a reservation, and I might have barged in on the restaurant skipping a line of 20 people thinking that they didn't have reservations, but I actually have no idea....
But hey, if it tastes good, it doesn't matter if its touristy, right?
https://www.trattoriazaza.it/en/