We have stayed here
http://www.sleepinitaly.com/rome/gianicolo/apartment-alessandro-poerio?r=s
and highly recommend. There is a bus stop right up the block, a taxi stand about 3 blocks away, restaurants, grocery stores, bakery, etc. all nearby. It is a neighborhood and you feel like a "Roman" there. The balcony is awesome, has laundry, only one floor up, all positive. It is further southwest than many like to be from the center but we did not find that a hindrance at all as the connections were all so easy to make. I'm working on our report (pesky job really interferes with my progress.....) but hubby has our little home page finally done-
http://home.roadrunner.com/~tomshirl/index.html
Click the Rome button and there are a few pictures from our trip this year.
If you are interested in finding out about this place we do have the owners direct email, just let me know if you would like it. The landlord was terrific.

Springermad,

Of all your suggestions, I like the location of the 2nd one near Ponte Sisto the best. The first is near the train station, and the third is just too far out - especially if it's your first time in Rome.

We generally stay in Prati when we head to Rome because we used to live in this section of town and have many friends there. It's a viable alternative - but I'd stay in the central area your budget will allow. Here's a link to the apt we stayed in - and some apt. tips - Good Luck: http://tinyurl.com/Rome-apt

I also like the second one best. For what it's worth, for some of my trips to Rome in the past, I've rented from realrome.com (relatively inexpensive apartments, great management!), cross-pollinate.com (inexpensive, I was a lot younger then), rentalinrome.com, vrbo.com, and one other place that is now out of business. Almost booked once with sleepinitaly.com; they were very helpful but did not have exactly what I was looking for.

We stayed here for a week last month. http://www.friendlyrentals.com/en/apartments/rome/apartment-4031-220.htm

It was worth every penny. Literally a couple of minutes walk from the metro and easy walking distance of many main attractions.

We will use Friendly Rentals again. They were brilliant.

We just returned home from our trip to Italy. We stayed in Trastevere and really enjoyed it. Here is the apartment we rented. Www.angelishouse.it. It was penthouse B. Buon Viaggio!