Any recommendations re where to stay in Rome

I'm taking my daughter on a 4 day sight seeing trip to Rome in April. We have been on various trips before and often found really nice B&Bs to stay in rather than hotel chains. We won't spend much time where we will stay so as long as it's clean and in a safe area we aren't that fussed about great facilities as we are going to see the sights not pounding away in the gym etc!
I have never been to Rome before so am clueless so any suggestions would be great. It might be handy to be quite close to the main train terminus for ease of getting about but not essential. I can of course use good (sometimes) Tripadvisor but maybe some GC members will come up with good places to stay. Thanks.

 

We went last September and stayed in an area called Trastavere, small streets, felt very safe, lots of lovely places to eat, walked to colosseum, Vatican etc. stayed in a lovely little hotel ( Santa Maria) with a small garden with lemon trees, found on Tripadvisor. Transport system wasn't wonderful, so didn't bother with buses etc as we walk a lot.

 

Wow thanks everybody, just going to do loads of searches now with your information, much appreciated. Have already booked the flights with Ryanair (groan but not hard on the bank balance and they fly direct to Rome from Edinburgh Airport). We're going in April so maybe it'll be too early for the Roses? but still looks a lovely spot to visit. Noted re buses!We went to visit Pompeii, Herculaneum and Vesuvius last year at about the same time and had a wonderful trip. The B&B where we stayed was the best we've ever stayed in. It too had lemon trees and they made their own limoncello which was free for us guests to drink whenever we wanted, hic! and very very powerful.

 

We had a city break a few Octobers back in Rome , fantastic place . We stayed opposite the opera house in the Termini area ( main railway station ). We flew Ryanair to Ciampino airport . I would strongly recommend getting the train into Rome . We booked the shuttle coach , and trying to get back to the airport in Rome traffic was impossible on a Monday morning. We had to hire a suicidal taxi driver To get around Rome , we booked a three day pass on the open top tour bus . We took the full tour on the first day , and used it for the rest of the weekend as a taxi . great value. You will know all the places to see , it is a very compact city centre . One top tip don't sit down at a cafe table with tablecloths , it doubles the cost of a drink ! Rome has been full of thieves and pickpockets for the last 2000 years , so watch your money and don't let anybody "help" you.