If you fancy going to Rome, go to Rome!
Do it the cheap way. Fly Ryanair from Stansted to Ciampino then get a terravision bus into Rome central station. If you book flights in advance they're nice and cheap (and I mean pennies for the flight plus taxes) and you can get from the airport on the bus for about 8-10 Euro.
I'd say it's definitely worth going for a central Hotel though, this is where it's worth spending extra cash. I stayed in the financial district and though it was a really nice 4 star hotel, it was a 3 mile walk or a 50p bus ride into the centre, plus there were no local restaurants or bars that were worth going to. Research hotel location very carefully. Go for one somewhere near the Palatine Hill, the Forum and the Colosseum as that's a good starting point for most of the stuff you'll want to see/do. You can get reasonably priced food from the likes of MacDonalds etc, but you really should go local and get a nice bowl of pasta or some real fresh pizza. It's all reasonably priced and the locals are fairly welcoming too. Also, go out for some proper ice-cream at a gelateria after you've eaten your dinner!
I have to say that personally I preferred Florence as it was more romantic for me and the GF and there was lots of arty stuff to see (like Michelangelo's 'David' at the Galleria di Academia and the Galleria degli Uffizi. There's ponte Vecchio and allsorts of Medici family stuff that's worth seeing too (they were one of the big families.
All in all, it's worth seeing and if you want to go, you should do it!