When in Rome…

We are thinking of booking a week-long holiday in Rome towards the end of April. There’s lots of hotels to choose from, all over the city — but I’m wondering where we should book. What’s the best part of the city to be? We don’t need to see the Colosseum from our hotel room window, but I don’t fancy having to travel half an hour by train to get somewhere interesting!
I’m also wondering about the weather. Are the temperatures bearable then?

And I know that some of you have been there (or even live there!) — any tips?