Welcome aboard the RoadTrip America Forums!
Without repeating myself too much, here's a post where I talk about some of what I consider the best possibilities in that general area. Be sure to follow the link to the discussion of a drive through Massachusetts, and also have a look at these posts about New England.
If you really want to see America, I'm afraid you'll have to do it by car. Our public transportation system, particularly the trains and busses are not quite up to the standards you have in the British Isles, particularly in terms of frequency of service and coverage. Hostels exist in the U.S., but while there are fewer of them here than in Europe, the ones I've seen tend to be fairly good. I have no idea what a 'trap' is.
Beer tends to be moderately cheap here. It will help that the pound and punt are worth so much against the dollar. One option is to try the pubs connected with small local breweries. These often have local musicians on certain nights. Inquire locally.
AZBuck