We stayed several times up on the Aventine Hill and it is lovely up there but a rather long walk home at night. I used to heed the advice "don't stay near Termini" but on my last few trips, I've stayed within walking distance of the train station. It is convenient and there are quite a few choices. Hotel Sonya should be in your price range. Many many restaurants nearby. I have rarely felt unsafe in Rome, even late at night with my adult daughter but I am wary of pickpockets as we have seen them "at work" several times in the city.

Another area I would like to stay in one of these days is Trastavere so you may want to explore hotels in that area.

Last time I was in Rome, I stayed at Residenza Cellini. It was a comfortable hotel, very reasonable and good value for the money. http://www.residenzacellini.it

I love the Hotel Modigliani.

Residenza Canali ai Coronari is a true little gem. is Near Piazza Navona..My grandaughter and me spent four days in this lovely pensione.
it has excellent reviews from Trip Advisor.

http://www.residenzacanali.com/?lang=en

A strong second for Residenza Canali ai Coronari.

Well within your price range. In spite of it's super central location, it's on an auto-free street which is very quiet at night.

ttt

Trastevere.

http://www.arcodellauro.it/?lang=en

www.hotelmodigliani.com/

Another Modigliani fan here, for many years. It' a winner, on a very quiet street leading to Spanish Steps one way and the other toward Trevi...and Via Veneto. Walk to Navona in 15 minutes. One stop for Coliseo.

I am staying at www.relaismaddalena.com/ when I arrive in Rome next April. It is near Albergo del Senato but is a little less expensive and has received outstanding reviews.

carolsc

Another Residenza Canali fan here, my DH and I loved it here so very much! Enjoy!

My husband and I just returned from a stop in Rome. This trip we stayed 3 nights at the Hotel Grifo in the Monti area. We loved it. It is a neighborhood rather than a tourist area. Small restaurants, bakeries, grocery stores, produce shops, gelato shop, etc. all with a block or so. Just a few blocks to the Coloseum. Rooms are small (typical European), but the fifth floor has a room that opens out to a balcony. Balcony can be used by any guest, however since the elevator only goes to the fourth floor, most guest don't find it. Well within your budget. Staff is so nice and helpful. They treat you like family. I would not hesitate to stay ther again.

Have fun in Rome.

I recently stayed at Massimo D'Azeglio. It is very close to the train station and about a 15-20 minute walk from the Coliseum.
http://www.romehoteldazeglio.it/en

The place me and my wife stayed was Maison Giulia (address Via Giulia 189A, Navona, 00186 Rome)great apartment very affordable, close to piaza navona, campo de fiori also close to trastavere . I would go out on a limb and say the best location for visiting rome. Apartment was very modern and new, no smoking with a full kitchen. staff was very friendly

Just decided to return to Rome next September, but only for 2-3 nights this time so we're going to stay in a hotel instead of an apartment for a change. Ill be looking into these for sure!