Just got back from a long weekend in Rome, and have one rave recommendation and one thumbs down. The rave is a restaurant called the Glass Hostaria in Trastevere. The chef is a woman named Bowerman, and the food is out of this world. Perfectly balanced flavors and textures, you find yourself closing your eyes to take it all in. Reasonable wine list, and modern but relaxing decor. With a sixty euro bottle of wine (brunello from Altesino), and two glasses of franciacorte to start, the price was 200 euros for two. So it's a splurge, but by far the best meal we had in Rome - in fact, the best meal I can remember having anywhere.
The thumbs down was Hostaria Romana, off the Via Tritone. Very popular and crowded, and gets a lot of print on chowhound and elsewhere, and the food is lousy. I had a tortellini in brodo that was so salty I sent it back - obviously made with soup powder. The rest was, I have to say, typical Roman restaurant food - indifferently prepared, cheap ingredients, often just stuff thrown on a plate, relying entirely on animal fat for whatever flavor there is. There's a lot of bad food in Rome, so you need to do your homework.
One more recommendation. There's a new mozarella bar called Opika, with two locations. We ate at the one in Campo di Fiori. Food was tasty, you can eat light (not always easy in Rome), and not too expensive.