Yes, you do well to avoid the Termini area.
For is a list of 3 star hotels in the center of Rome see central Rome hotels .
They have been selected from tourist reviews based on value, service, location etc. Hotels marked with a star have received consistent good reviews.

If you are considering the Trevi fountain area, then I would advise you to also check hotels in the Spanish Steps, Pantheon and Piazza Navona areas to compare prices.

For hotels near Trevi see Trevi fountain Rome hotel .

You can also consider the Trastevere area, it's across the Tiber River, close enough to Rome's best tourist attractions - a charming neighborhood of Rome.
Enjoy!