The Black Swan room at Together was perfect for our stay in Rome. It's well located (about 25 mins walk from the Colosseum) and in a really buzzing district, with lots of great bars and restaurants.
The hostel felt very safe and had a great vibe about it - I was travelling with a friend, but it seems like a great place to travel on your own as well, everyone was very friendly.
The only downside is it can get quite hot during the night and noisy early in the morning.