There are two home teams in Rome, Lazio and Roma. They share the same stadium, Stadio Olimpico.
The week you'll be there, matches are played on the 13th. Roma is away but Lazio is playing at home against Siena. As far as tickets, I have no idea. PM Licurgo, he's a soccer forum regular on here who lives in Italy.
I'm jealous man, that trip should be a lot of fun. I hope I get to see a Serie A match one day.
For the tickets I can help you to buy them on Internet.
Here there is the official website of S.S.Lazio: http://www.sslazio.it/cms/view (it is all in Italian, I can help you). The game could be played on April 12( at 6 pm or 8:30 pm) or 13( at 15:00 or 20:30).
I think that they will sell your tickets on the finish of March
I'm just back from a weekend in Rome watching the International rugby and a group of us were going to catch the big Roma v Milan game that night but ended up getting p*ssed in the Piazza Navona and watching it on TV instead..That game was a top of the table clash and yet still wasn't a complete sell out so you will get tickets for Lazio/Siena no bother.Keep your wits about you and you'll be fine.
Rome is absolutely one of the most incredible cities on earth...after a while the ancient and historic wonders and masterpieces are so routine on every corner that you start to think 'oh yeah there's another 3,000 year old Fresco by Michelangelo,very nice'
Take in the Basilica of St Peters(it's worth climbing the 300 odd steps for the view both inside the dome and out over what is a beautiful cityscape).And the Sistine Chapel of course.
It's all easily walkable so Trevi Fountain,Spanish Steps,Pantheon,Forum,Colosseum and The Vatican are all doable on foot