In general, you'll not find many places to exchange currency in the US with anything other than steep fees, and a larger-than-expected spread between buy and sell. In particular, US airports are notoriously expensive places to change currency.
It might be more affordable to exchange some pounds for dollars before leaving home---possibly by mail (
http://www.moneysupermarket.com/travel-money/). When I travel, I tend to carry my bank card with me and use it to withdraw local currency from an automated teller wherever I happen to be. That's not the cheapest means possible, but it is often better than an in-person exchange, and very convenient.