Hotels in Rome

Sounds like you need a good guidebook. I highly recommend the Rick Steves one for Rome. Also, you need to define in euros what you mean by "moderate."

Do a bit of research on booking.com and tripadvisor.com. You can input all of your parameters.

A lot also depends on how long you plan on being in Rome and what you plan on doing and seeing while you're there. Rome is a pretty big place and there are nice moderately priced hotels all over the metropolis. Sitting down with a good guide book to figure out what you want to do and see seems like the logical first step. And Rick's Italy and Rome guide books also have hotel recommendations by price range and neighborhood.

In Rome I always use public transportation and also love to walk.
I stay near the Central train station and there are several nice moderate/budget hotels within just a couple blocks of the train station.
Even as a single woman traveling - I did not feel any trepidation about walking from the station to my hotel day or night.
I have stayed at Hotel Sonya, Hotel Contila, Beehive (more of a hostel type room)
You can go onto TripAdvisor.com and choose the location Rome train station and see lots of hotels, they also post their prices. but on tripadvisor you can look at photos, see the rooms, and read lots of guest reviews.
I would recommend contacting the hotel directly to make a reservation, sometimes you will get a better price than listed on TripAdvisor.

We need some help and you need to do some research. Go to your public library and check out some guides and travel DVDs on Rome. Better yet, view the Rick Steves DVDs on Italy and Rome - there are several. You need a much better understanding of Rome in general.

.....moderate hotels in Rome.....
You are going to have to define "moderate" for you. For us, in Rome, moderate is about 200 Euro/night. Are you comfortable with that?

........We will not have a car. .......
Nobody in their right mind has a car in Rome so that has no bearing. If staying in the suburbs, it does.

.........Also prefer breakfast include.......
Most hotels include breakfast so there are probably a couple thousand hotels that would meet your criteria.

You need to decide what neighborhood or where in Rome you want to stay -- probably fair more important. We always stay in the Termini area for convenience to local transit and nice local restaurants but it is a busy area that some don't like. The hotels that we have used in that area are - Hotel Sonya across from the Opera House, Aberdeen, and Contilla very close to the train station - Termini. We prefer them in the order listed. Wife believes that the lattes at Sonya are better. We generally use the Contilla when passing through for one night and because a self laundry next door. Important at times.

Hotel Aberdeen is a nice, clean hotel. It has a great breakfast and nice staff. I have stayed there twice on week long RS tours. It is near the train station. It is in walking distance of several wonderful churches and right near the metro.

I have also stayed at the Hotel Selene on a BOE tour and that is just a few blocks away. Very nice hotel, but more money. You do not need a car in Rome. I liked both hotels and would stay at either one but Hotel Adberdeen is less expensive.
Both include breakfast in the price.

I have stayed at the Hotel Aberdeen and would stay there again. It is located next to the Ministry of Defense. We always had a lot of police by our hotel. I never worried about returning late to the hotel. It was about two blocks from the Metro.