For the newbies, a minimoon is a shorter, cheaper version of a honeymoon, often done immediately after the wedding but with the intent that a more elaborate honeymoon will be happening sometime down the road.
DH and I went to Washington D.C. We didn't plan it all, but just went wherever we found the cheapest flights. We spent under $1000 for the two of us on hotel, food, air, and attractions.
I've also heard Gunflint Lodge is nice and Blue Fin Bay Resort, both upstate.
So...
Washington DC
Gunflint Lodge
Blue Fin Bay Resort