Agreed Avios seem ideal given that you're in an American hub and geographically close to a lot of great destinations.

Here are some examples (round trip price, in Avios)
15,000 - Miami, Chicago
20,000 - Los Angeles, DC, San Jose (Costa Rica)

Keep your eye out for Amex and British Airways credit card offers. These have been available for as much as 100k each (the 75k offer mentioned previously is now dead).

The Citi AA thread has links for a 50k Personal card and a 50k Business card (and I believe a 30k Gold card that may be gotten at the same time).

One last thought -- once you have a few signup bonuses under your belt, you may want to consider a 2% cashback card for ongoing spend (such as the Fidelity Amex). Avios can provide great value for short distance trips, but in general it's hard to get much more than 1.5 - 1.75 cents of value per mile for domestic, Economy travel. 2% cashback is a guaranteed return, and paying for the tickets gives you complete flexibility on dates, airline, etc.