You have me puzzled, What does your age have to do with renting a motel room? I'm 59 and rent motel rooms all the time... Actually I pretty much live out of motel rooms. Renting one for one night is not uncommon, why would you feel awkard?
How can I being 66, rent a motel room for a night,without being awkward?
Rent the room on priceline. Do one of their quick deals. You pay in advance, so all you have to do at the hotel is give them your name. Now you've got your key card, the room is yours for the night. Since it's prepaid, there's no going back to the counter. Just leave the key card on the dresser in the morning and leave by the checkout time.
Everything is online these days. Book it online, show up, tell them your name, and ta-da you have a room.