I love remoteness. It can be very expensive or very cheap. Where I live is very close to campgrounds where you are the only ones staying, where you can go for long walks and not see another person. We have been going away for 2 nights at a time to places like this. Campgrounds with minimal facilities, where you can sit by the fire at night gazing at the Milky Way in all its glory. Admittedly, the facilities are primitive - pit toilets, fire rings, and picnic tables are often provided, but you bring your own firewood and water. No electricity or mobile phone coverage also means a lack of internet. Being from Australia we’re used to having fewer people around - after all, we’re a country a similar size to the contiguous US, with a population of a bit over 25 million.
But at $6 a night within less than two hours of home I can think of a dozen such places. All worth visiting more than once.
I’ve also wandered around remote parts of the country for weeks, alternating between staying at remote national parks and a day or two at camping grounds in towns where I could do my laundry and buy supplies for the next part of the trip. These expeditions were also cheaper than living at home. I’ve done something similar in the US, where I hired a car in LA and visited 23 national parks, including Death Valley, Bryce… staying at campgrounds all the way. Once I was actually in the US it was quite cheap, but much more crowded than what I prefer.
Of course, you can go to the other extreme, and fly to the other side of the world and be remote. I’ve done this too. One year, a trip to Iceland and Greenland (including a ferry up the coast). The next, a trip to eastern Canada including a ferry up the coast of Labrador. A trip through Chile from the Atacama desert to Patagonia, including Easter island. And then a trip to northern Canada - Nahanni, kayaking with icebergs in Nunavut, belugas in Churchill, camping in tombstone park In Yukon, driving ourselves up the Dempster highway to Tuktoyaktuk. Getting to really remote, far off places isn’t cheap.