I liked staying at the Fifteen Keys, which isn’t too far from Termini Station.
My room was around $300 a night. Prices may have gone up. https://fifteenkeys.com/
If I was choosing by neighbourhood, I would probably prefer staying a little closer to the Spanish Steps, Travestere or the Jewish Ghetto. I chose the Fifteen Keys because I wanted a Boutique Hotel that was walking distance from the main train station on that trip.
There’s a food hall called Mercato Centrale, attached to Termini Station, which orders Bonci pizza by the slice, as well as round pizzas. Those were the best pizzas I found on my trip in 2017.
My only high end meal in Rome was at Roscioli, which I definitely recommend .
I want to visit Armando al Pantheon some day.
Lots of threads on this board.
Roscioli Salumeria con Cucina [Rome, Centro Storico]
Armando al Pantheon [Rome, Centro Storico]
Time flies.