Is there a good tow vehicle that also gets good MPG?

I would look at a gently used Nissan Pathfinder (pre-2013, which is when its redesign ruined it, IMO). A properly equipped Pathfinder (years 2010-2012) has a tow capacity of 6000 lb. Also look for a gently used PUP under 3500 lb. With this combination, you should be fine.

I get 20.5 mpg not towing (highway driving at speed limit) and when we had our Aliner, I got 16-17.5 mpg towing. You need a larger/heavier PUP than our Aliner, but you should still get at least 15 mpg towing.