It looks like there are already two other websites that provide this function for both London and New York.

For London:

http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2?language=en

Looks like it allows you to search for addresses, stations, post codes, and points of interest.

For NY/DC(Beta)/Boston(Beta)

http://www.hopstop.com/

This looks like it allows the user to search for addresses, intersections, as well as Points of Interest. It also has a mobile service that allows you to text and figure out public transportation directions. Seems like this would be handy for tourists.