Long but leisurely trip from NH to NM up to MT then home

I would just concentrate on the southern part of your trip. April is just too early for the high plateau northern states. Add Taos to your itinerary if you prefer interesting towns, check out the Taos Pueblo and there are plenty of other interesting places in NM. Carlsbad Caverns in southern NM are another possible place to visit.

Allow 4 or 5 days each way for travel time and that will give you over two weeks in NM.