Rome - recommendation of best area/neighborhood to stay/eat wanted
A great neighborhood to stay in is Monti. It's very centrally located, but not touristy at all. The Apollo hotel is great, low priced place to stay. Higher end try Duca D'Alba or Ceasar House. Very high end Inn at the Roman Forum.
Restaurants in Monti:
Taverna dei Fori Imperiali
Al Vino Al Vino (wine Bar)
Cavour 313 (Wine Bar and Restaurant)
Faifiuche (wine, beer plus food)
Via Urbana, 47, Rome, Lazio 00184, IT
Look around the area of Prat. It is just beside the Vatican & Castel S.Angelo and you can walk across the Tiber to the old part of Rome and avoid the tourist area. There are lots of nice restaurants and Pizzerias and best of Rome's icecream shops here. There is a nice covered food market in Via Colle di Rienzo.Lots of little hotels too.
Trastevere is a good idea, another could be the more central parts of Prati. The very touristy Campo de’ Fiori area has good food. But actually, the totally untouristy often modern peripheral quarters (some bourgeois, some working class) have excellent trattorias and food shops. There are municipal markets in every neighborhood (you could do a search for mercati comunali).