There are two and cheap - one of the youth hostels in Rome is very close to the Olympic Stadium (the one where Lazio Roma and AS Roma play their soccer home matches

)
It's called in Italian: Ostello della gioventù
http://www.mediterre.net/ostelli_della_gioventu.htm
Ostello OIKOS - Via Paolo Renzi, 55 - tel. 06/5080280 - fax 06/5073233
e-mail:
[email protected] -
http://www.oikos.org/ostello.htm
Ostello AIG Foro Italico - "A.F.Pessina" - Viale delle olimpiadi ,61 - Tel. 06/3236267 - fax 06/3246613
Aperto tutto l?anno - posti letto 334 (meaning open all year long, number of beds: 334)
Hope this helped
