We are taking Terravision bus from airport to Termini station then catching taxi to Flaminio Parioli region of city. Are taxis readily availabe at this bus drop off and how much should we expect to pay?
Take a taxi direct from Ciampino. There is now a fixed rate for rides from Ciampino to the city center of 30 euro (40 euro for rides to/from Fiumicino). Terravision is 8 euro per person plus a taxi ride to Flaminio is anywhere from 8-15 euro, depending on the exact location. Do the door-to-door service.
There are taxis right outside Termini station, you can't miss them. My taxi ride from termini to my hotel near the spanish steps was 10 euro (with luggage), if that helps.
Be sure to look for the little taxi sign and get in LINE for a taxi. When I walked out the Rome station there were taxi's EVERYWHERE. Rick cautions in his book to make sure they are official, but even the fake one's look REALLY official! This one guy just kept asking me if I needed a taxi, but he was so eager that it made me suspicious and I asked for a price quote, to which he quoted 30 euro. Which is crazy and I walked away. So I learned after that to always get in the taxi line! Good luck and have fun!