Ciao capyoda. It sounds like your checking the right sites, Tripadvisor has rental listings too.

I was just going to say, IMO, Rome is small so any rioni in the centro storico would be great. (I don’t mean to be presenting myself as an expert. My story is: I’m in love with Rome and I’m about to go back for my 13th time - I think it’s my 13th, I'm losing track. I do tons of research for myself so I’ve been trying to share here since I’ve benefitted by others so much. So this is just one subjective opinion here)...

..A very rough outline of the Centro Storico would have the northern boundary at Villa Borghese, southern boundary at the Colosseo, eastern boundary at Termini Stazione (the train station), and the Tiber could be the western boundary. But there are also lots of rentals west of the Tiber in the Vatican area, and southeast of the Vatican is Trastevere. Trastevere could be a terrific place for you. It's right across the river from Campo di Fiore, very lively. The Monti area is well regarded it seems by Slowtravelers. A little north/south/east/west of these areas would be fine too - check where the metro stops are tho. (There are only 2 metro lines that basically make a cross through the center of Rome). If your apartment was a little outside of this area but you were close to a metro it would be fine (like the apt Bamavol just found west of the Vatican). And Rome is very well served by bus lines - if the metro wasn't right outside your door. But I'd steer clear of anything much further out than this - you'd then be in the suburbs of Rome which is a whole different beast.

Google maps is your friend. (Well it's my friend). Use the satellite view and zoom in. You'll see all the landmarks - the Pantheon, Colosseo, Piazza Navona, Trevi Fountain, etc. When you see an apartment listing you like, plug in the address and see where it is in relation to everything. Google street view is awesome. I think I'm getting addicted. You can even use the street view now in Pompeii. So again, when you see an apartment that's well reviewed and the price is right, click on Google's street view and "walk around".

In general, the area around the train station might have sketchy areas - but that's also where there are tons of hotels.

An interesting thing to keep in mind in terms of safety is that it's a capital city with tons of government buildings - which are all highly surveilled and protected. I befriended a few Romans, and one young lady said she always felt safe because of all the security personnel.

Another thing about using streetview on google: I'm currently trying to readjust my reaction when I see graffiti. I live in Los Angeles, and when I come across areas here with alot of graffiti - I don't feel safe. But in Rome, using google's street view, I'm seeing tons of graffiti! I haven't been to Rome in 3 and half years, but I don't remember that much graffiti. I've been "virtually walking around" Monte Mario where I'll be staying (that's where the Cavalieri Hotel is) - and there's graffiti. I've been checking out the Aventine for my sister, she's considering staying at the Villa San Pio. And there's graffiti on view. And these 2 areas are considered upscale residential neighborhoods. I know Rome's graffiti does not have the same criminal connection that it does here in L.A. where rival gangs use it to tag an area. (Just thought I should share this in case you come across it and have the same reaction to it as I do, I mean did...)

Don't know if I actually helped in anyway..... but that is always my intention.

Good luck with your research, post back when you find stuff you want opinions on, etc.