You've not stated which Rome airport your transfer will be at. If it's Fiumcino, the fastest way into the city centre is to take the Leonardo Express train to Roma Termini station. Trains leave at 7 and 37 minutes the hour, with a journey time of 35 minutes. (The return trains leave at 22 and 52 minutes past each hour).
That would give you very little time (if any) to see any of the sights. The Terravision bus would probably take much longer.
From Ciampino, the only direct route is with Terravision which, (like the journey from Fiumcino) is likely to get stuck in Rome's traffic. The alternative involves taking a bus and then connecting with either the train service or the subway. Neither route is particularly fast.
If you did decide to take the Leonardo Express, from Fiumcino, this map is centred on Termini station. By clicking on the neighbouring maps, you can see which attractions are nearby:
http://en.reserver.it/rome_map_6.html
Chris