The most amazing place I have ever stayed in four trips to Roma was Villa Magnolia Relais. It is very reasonably priced for everything you get. The host is magnificent and friendly. The rooms are luxurious beyond the price point and the best is the location. It is hidden away in a quiet area so it feels as if you are nowhere near the centre of the city and yet it is waling distance from the Vatican City. It is also over the hill from Trastevere within very easy reach of everything by bus/tram. You won't need to get an expensive taxi. The owner and manager is extremely informative and guided me to the most amazing restaurants off the beaten track. You have secure parking, it is quiet and there is enough space and a garden if you have kids. I hope you enjoy it.

Bettoja Hotel Mediterraneo near to termini station, easy access to city's sightseeings by walk from this hotel.

We just got back from Rome yeserday. We stayed at the Holiday Inn Express Rome San Giovanni in San Giovanni off the Metro A line. You can either get off at the Punto Longo station or the Furio Camillio, from there it is a 7 minute walk to the hotel. We found it to be safe and saw many tourists/families staying there as well. We found the reviews on Tripadvisor to be very helpful. The rate we paid was about $135 USD a night. It also includes breakfast. The only downside is the internet, thought it is free it was painfully slow. But the A line train is about 10 minutes to most of the popular site. We booked a private tourguide and a spent a whole walking and learning about the city. Hope that helps! 

You should check out the Smart Hotel. It is centrally located a few blocks from Stazione Roma Termini for quick access to all of Rome and the main sites you will want to see. It is new and thus very clean. Great service and if you include the breakfast as part of your stay you will not have to worry about getting up early to find a place to eat. My wife and I stayed there for 4 nights in September and would definitely go back if we make our way to Rome again.

I stayed twice in Best Western Art Deco hotel. It is close to @Stazione Termini. I guess there is more central location but this one was quite good for me. The hotel price was affordable and breakfast included. 

Close to the hotel there is a good trattoria @Mamma Angela's.

Borromeo Hotel Rome was a favorite of mine. It was a short walk to the Colosseo, which is a must see site. Having the easy walk to this attraction was great because we could go see it during the day and night. You can also purchase a tour bus pass that will take you to all the main sites. 

What we did was walk to the Colosseum, catch the tour bus, and jump off whenever we hit the next site we wanted to see. I remember the tour bus being around 25 Euros for 48 hours. I recommend City Sightseeing tour company! 

Here are some articles from my blog you may like. Happy travels! 

How to Explore Rome 

Which Tour Bus Do You Prefer: City Sightseeing or Trambus Open

With this price you can find good hotel like:

Residenza in Farnese Hotel Ponte Sisto or Hotel Lunetta

Francesco