My son and I stayed at Hotel Aphrodite right across the street from Termini. A small but attractive nicely-decorated room. Light woods. Two beds and non-smoking as requested.
www.hotels.com and I think it was about $90. Spotlessly clean. The wake-up call came on time. Desk was cheerful and helpful. Gorgeous glass mosaic tile in the bathroom. Comfortable beds. Breakfast included. I thought a pretty fine deal. Since we had that 1:45 am wake-up call, we missed the breakfast but did have get 4 or 5 hours of sleep and a place to be earlier in the evening.
Romelle