If you don't mind the wait for tags the moose hunting in Maine and New Hampshire is very good. The drive there from my home in Chicago is only about 24 hours (I have family there) and the benifit of not crossing an international border is not to be understated.
Both animals can be taken from Alaska and if you plan corectly you could get away without a bush plane and still hunt in the roadless interior. The Alaskan rivers can float a decent sized boat so you can arange for someone to launch you a good distance upriver and you can hunt back to where you started. I've only done this on fishing trips on the Anderscoggin river in New Hampshire but I'm sure the concept will work for moose and caribou. Moose like rivers anyway and having a boat could come in handy if the 1,600 pound beast decides to expire in water.