Italy - Which district of Rome to live in?

I'll be living in Rome for one month from mid March to mid April next year, and am seeking advice on the best district to rent an apartment as I've never been there before. Desirables:

- In the city centre.
- Close to plenty of restaurants.
- Close to a Metro station.
- Close (via Metro is fine) to tourist attractions.
- No need for parking as I won't have a car.
- Quiet street if possible.
- Doesn't needs to be particularly large as I'm on my own - one bedroom is fine.
- Budget is in the region of €4000 per month.

Looking on other sites, I've seen Prati and Trastevere mentioned a few times, which do look interesting, but I'm open to other ideas...

Prati would be ok. Trastevere is quite a wide area, there's no underground/overground in the proper Trastevere.

I'd consider other Rioni (http://en.wikipedia.org/wiki/Rioni_of_Rome) too, like Rione Monti (http://en.wikipedia.org/wiki/Monti_(rione_of_Rome)).

Furthermore, with that budget & apt size I'd not rule out that you may find some opportunity also in the most 'central' areas like Rione Ludovisi or Trevi.
You can find a map of the Rioni within the so-called 'centro storico' here:
http://www.comune.roma.it/wps/portal/pcr?jp_pagecode=rioni_quart_mun_i.wp&ahew=jp_pagecode

Thanks Alice, that's useful information.

I'm partial to Trastevere ;). In all seriousness, it really has everything you're looking for. On the other hand, at 4000/month, you can really have your pick of Rome for a one bedroom.

In Trastevere you're offered a taste of Roman life, proximity to attractions without the normal glut of tourists, the possibility for silence (pick the right street), and good eats. Prati is another good place but not as quiet as Trastevere (in my opinion). Parioli is a nice area as well but you're a bit removed.

Thanks!

How busy/noisy is the area around the Pantheon?

The area around the Pantheon is very touristy so it can be noisy and busy (like most of the Campo Marzio), but it really depends on which street you're on. It can go from being a river of people to a quiet side alley in a few meters. Just beware of bars / pubs nearby for the noise factor.
And I wouldn't be too married to the metro, it has a relatively limited reach and is really most useful for traveling long distances. Also, personally not a big fan of Prati, and like Trastevere a lot (FWIW my father lives there).

Thanks! I've heard good things about Trastevere elsewhere, so will look into it in more detail.

Monti is also very nice, but as the name implies, be prepared to walk up and down some hills.
Also, Trastevere can have a very different feel depending on what side of Viale Trastevere you're on. The S. Maria in Trastevere side is more lively and a nightlife destination, the Piazza in Piscinula side is much quieter, though there are numerous exceptions on both sides of that equation.
Good luck with your search and I'm sure you'll have a wonderful time wherever you end up - April and May are IMHO the best times of year in Rome.

I suggest you to consider Aventino, too. Quiet, central, near the underground stop (Circo Massimo - line B), lots of restaurant and many attractions nearby.

Do you have a flat already lined up? If not, the accommodations available may help to sway things. I spent Mar-Apr in Rome in 2000. Albeit, my proximity to work was important, but t was ultimately lodgings that decided the location- in the Monti, btw.

I suggest you to consider Aventino, too. Quiet, central, near the underground stop (Circo Massimo - line B), lots of restaurant and many attractions nearby.

Agreed, but even though it's close, it's not walking distance to the centro, which is what I would be looking for in a short-term rental. But for longer term it's a lovely area.