better area to stay in rome...near borghese gardens or near vatican or travestere

PapaVista is next to the Vatican Museum, Golden is next to the Villa Borghese gallery. Both are quite a walk from the other sights, therefore, unless you love to walk a lot, you'll need to rely on the buses or the Metro (papavista is close to the Ottaviano Metro station). These two hotels are in relatively newer areas of Rome which were build at the end of the 19th century.
My preference always goes to Trastevere, an ancient medieval district that is full of nice restaurants and has a lot of character, with small alleys that will make you feel like you're thrown back to the middle ages. Some of the best restaurants in Rome where locals go are in the Testaccio area, which is not far from Trastevere.

There really isn't much to see right around Villa Borghese, and it's a bit of a walk to transportation. When I was in Rome I stayed near the Barbarini metro stop, so it was easy to walk to the Spanish steps and Trevi fountain, plus there were plenty of options to get around via metro, bus, or taxi. Next time I'll be staying closer to Termini, since it's only for 1 night.

The Vatican area (Prati) is a lovely and convenient choice. Very easy to connect to the rest of Rome via bus, metro or tram. It is my favorite area for shopping and dining. Trastevere is cute and interesting in a way, but Prati is where a lot of professionals live and has a quiet character at night. It's only a 20 minute walk to Piazza Navona. I live near the Borghese and can point you to many restaurants, but I think you'll like Prati better. The key is walk ability and access to transportation she you need it, plus charm. :-)

elaine,

If you decide to stay in Trastevere, I'd highly recommend Casa San Guieseppe. It's in a very convenient area near Piazza Trilussa, and within easy walking distance to many restaurants, etc. It's a bit "distant" from Metro stops and some of the more popular sites, but there are Trams and other transit available.

Did you consider the real center of Rome? Maybe near the spanish steps, pantheon or trevi?
trastevere is too far from the center and it is very easy to get lost. during weekend it is also very noisy, often with drunken people shouting (personal experience!)

Trastevere is just a bridge away from the historic center of Rome (Piazza Navona, Campo dei' Fiori, Pantheon) and it's a great place to stay or visit. Some great restaurants there as well.

Villa Borghese is near the Piazza del Popolo and Via Veneto areas. Restaurants are pricier and it's a hike (although downhill) to the historic center if you decide to walk. Very different feel than Trastevere. Personally I prefer to be closer to Piazza Navona, so of your choices, I would choose Trastevere.

Put me down as a Trastevere fan as well. If you stay deeper into Trastevere there is a tram every few minutes that takes you right to Largo Torre Argentina, a nice central location in the heart of Rome.