These recommendations are from a Roman friend (hence why the plural forms are in Italian), including emoticons. I am working my way through this list so only have comments for those places that I have tried so far.
BAKERY Panella – Via Merulana, 53 and Via dei Gracchi, 262 
very ancient bakery in Rome, bread, pizza, cakes, dishes, bio, biscuits … yes, I agree. They had lots of variety and items that I had never seen before.
Campo de’ Fiori – Piazza Campo de’ Fiori, 22 
very nice and noisy bakery to buy warm pizza alla pala, bread, cakes, biscuits … it’s so so so so famous. It does have lots of stuff and they are accustomed to tourists so don’t even try to speak Italian in there.
Forno Monteforte – Via del Pellegrino, 29 bread, bar, enoteca, cakes – very friendly … my favorite so far. It’s elegant, recently featured in Vogue Italia, and quite delicious.
DELI
Natura Sì – Piazza Farnese, 99 -100 only Bio food the store is ok, but people are 
… It is the organic store for Rome.
Castroni – Via Cola di Rienzo, 196/198 
plenty of delicatessen, and sweets, best in Rome … this is an emporium, a treasure land for ingredients and products from all over the world.
Le Sicilianedde – Viale Parioli, 35 all food is typical from Sicily and next door there is the Gelateria the ice creams and pastries are……
GELATERIE
Ciampini -Piazza San Lorenzo in Lucina, 29
DaRe – Via Bisagno, 19 5 mn from my home very, very tasty icecream
Gelateria dei Gracchi – Via dei Gracchi, 272 … They do have real vanilla flavor. It’s not glamorous and I wish they would make fresh gelato for the evening.
Pizzerie
Emma – Via Monte della Farina,28 the best pizza in Rome … I don’t know. The pizza was thin which is the Roman style. The restaurant is a large, but light, cavern underground. Very touristy as it is a stone’s throw from the Roscioli bakery.
Mora – Piazza Crati, 13 pizza and tuscany restaurant
Trattorie
Da Bucatino – Via Luca della Robbia, 84 – very noisy restaurant but the food is fine, typical roman cuisine … I liked this place. The waiter was a bit too fast and not so good at upselling but the food was good. Because the location is in Testaccio away from the tourist center, the crowds are not quite as bad here.
Hosteria Grappolo D’oro – Piazza della Cancelleria, 80 food and fantasy… right near the Campo de’ Fiori. Food was fine but nothing I would go in search of.
Enoteche
Il Goccetto – Via dei Banchi Vecchi, 14 wine, wine and very friendly place
Del Frate – Via degli Scipioni, 122 excellent enoteca and very nice restaurant
The place of my heart:
Hotel Locarno – Via della Penna, 22 Beautiful liberty hotel from 1922, with original furnishings, there is small nice garden and lovely roof garden, the cocktails are super and in winter they light the fireplace, also the restaurant is quite nice
And in the end: Hotel de Russie – Via del Babuino, 9 very luxury hotel, but don’t miss visiting the garden is absolutely beautiful and maybe to take a coffee, or cappuccino or even a cocktail, with credit card……
I have other lists so I will publish them later. Eventually, I’ll have my own list of top restaurants, but for now, I’m not sure…