Renting Apartments in Rome - which neighbourhood and any recommendations

The Campo Dei Fiori area is great - if you stay just a little off the campo. I stayed in an apartment half way between Campo and the Pantheon and loved the area. It's walking distance to the Forum, Piazza Navonna, Spanish Steps, Trastevere and lots of great restaurants. Just don't pick an apartment directly on the Campo and you will be fine. I would suggest the apartment I stayed in but it was just one bedroom. There are many, many in the area that are bigger.

My family of 4 will be in Italy late June/early July, and like you have used VBRO.com to get apartments.

The apartment we are staying at in Rome is in the Spanish Steps area.
I was considering Trastevere, but after mapping walking distances, decided the Spanish Steps looked to be easier to walk to everywhere from. (That is just my guess.)

I found the apartment through VRBO.com, and it is just one of a number under the same management.
http://mymagicrome.com/index.html

I emailed with Fabri there and he was extremely helpful with all of my questions and arranged for a car to take us to the airport for departure Sunday morning.

Perhaps one of his apartments will work for you.

I don't rent apartments (travel solo and it's not a vacation if I have to make the bed), but friends rented in the Jewish Ghetto just off Via Arenula and had a great apartment for four (2 adults, 1 son and 1 daughter). I visited them there and it was on a quiet street with all the amenities you listed. Across the bridge from Trastevere, very close to Pantheon/Piazza Navona/Campo dei Fiori.

Make sure that whatever apartment you decide to rent has Air Conditioning! You will need this in July! If you have AC, you can close the windows. The partiers won't be such a nuisance! I've usually stayed in the Prati (Vatican area) because it's mostly locals, and has a lot of transportation options to the areas I like to visit during the day, and the restaurants in the area are frequented by locals. Better food, better prices, as opposed to the more "touristy" areas. This is just a suggestion. I have stayed in Trastevere, and had no problem with noise, as we were tucked into a side street. Midnight is about my limit now! I absolutely love being at Campo diFiori in the morning when the vendors are in the piazza with their flowers, salamis, and other goodies, so if you have
A.C. or are on a side street, this may be a really great place to base yourself.

My family (of 4 including 13 year old twins) stayed in a wonderful safe apartment-- 3 BR, 2 BA (with washing machine), full kitchen, lovely living room, excellent WIFi, plenty of room to spread out in the Campo de Fiori area. The apartment is on a pedestrian walkway, with minimal noise. Across the pedestrian walkway (like a sidewalk) is the Hotel Ponte Sisto and a small grocery store (you can google earth it and look for Hotel Ponte Sisto). The location was terrific, right next to the Tiber's Ponte Sisto, which is the pedestrian bridge over to the Trastevere neighborhood and convenient when going to St. Peter's/the vatican. There is AC in the bedrooms according to the post on the VRBO website. Not sure if it will fit your budget, but we LOVED this apartment. I would also double check the # of beds in the apt unless you don't mind doubling up. I don't have any association with this apt, but we really enjoyed it so I thought I would pass it on.

http://www.vrbo.com/397029ha
If you have questions, please feel free to contact me directly.
SuzieeQQ

Thank you everyone for your suggestions. Much appreciated.

SuzieeQ - I did check out the apartment you suggested and it was already booked up. Looks lovely.

And Imyq - I'm going to email the owner and see what his prices and date are. His properties look nice and are in good locations.

I've managed to find a few nice places to check out in the areas in Navona/ Trastevere near the Ponte Sisto and near the Campo di Fiori (but not too close by). Things are booking up so I've got to get booking!

Thanks for the suggestions!