Before I purchased my first travel trailer I did a lot of back packing and tent camping from my SUV. I would usually camp for 3 to 4 days in the back country then find either an inexpensive motel or preferably a campground with camper cabins. This would give me access to a shower and usually a few other amenities such as pool or hot tub.
On a few occasions when I planned in advance I've used National Forest Cabins, but almost all of these have to be reserved in advance. My favorite is on the Greys River in Wyoming. No electricity but still has all the modern conveniences including a gas refrigerator, hot water heater, stove/oven and even propane light fixtures for $40/night.