Hotel Luxor is e good 3-star hotel located on the corner of Via Nazionale and Via A. Depretis. It's a pleasant 10-minute stroll from Termini station and public transport alternatives are plenty: Repubblica metro station is nearby and various buses run along Via Nazionale in all directions.
Rooms tend to be a tad small but they're clean, have all necessary amenities (including airconditioning) and breakfast is included in the price. There are various shops, restaurants and bars nearby and most sights are within walking distance.
Affordable option in a city where accommodation can be ridiculously expensive!