Can anyone recommend a cheap hotel, hostel or B&B in Rome that is in a safe area with public transportation?

Only staying in rome for 2 nights? What an atrocity to one of history's greatest cities! However if that is how long you are staying then so be it! Unfortunately ive traveled to rome about 4 times , its my second home. I may be wrong but at Fiumicino ive never seen any public transport to the heart of rome or termini, Fiumicino is pretty far outside the city center , let alone termini! Youll most likely have to get a cab, depending on how much baggage it will cost you heavily. Italian cab drivers charge you about 20 euros just for having heavy bags. As fas as lodging goes, if you want hostels to stay in they are very cheap! How ever all the hostels around termini are basically 20 person dorm rooms, where you have to be careful with your stuff at night. However, if it is a hotel you would like near termini, there is a very nice cozy hotel called Hotel Raffaello, right near termini. Cheap as well! I hope i help somewhat, enjoy your stay in rome!

Hotel Portafortuna near Termini Station like 5 min walk There is a train from Fiumicino to Termini station called the Leonardo Express its easy to find. http://lingeringirl.blogspot.com/

I stayed in the hotel I put the link I paid less than they require on the website, the only trouble thei had a concert in a nearby bar. you are at walking distance from the Pantheon and almost everithing