Ideas:
- You could always go on a camping trip together? Would probably be cramped and uncomfortable, though. And a full day and night out camping somewhere requires lots of effort for just a hookup
- Go for a walk in the woods/in the countryside, take a picnic blanket and food, find a secluded spot.
- Hotel is pretty good, and a single room for the two of you wouldn't be weird as anyone would probably just think you're friends
Not a lot of options if you want it private and houses aren't an option