As posted above, some programs will offer lodging the night before, and some won't. I've noticed that it usually depends on the specialty. A friend of mine applied to family med and had his hotel paid for on every interview. And then they gave him gift baskets or something and wrote HIM a thank you note. I'm not even kidding.
I applied to prelim surgery and radiology. Two of the prelim programs paid for a hotel, and one of the radiology programs paid for a hotel. I interviewed at about 25 rads programs and 5 prelim programs. My wife applied to ortho and didn't have any of her hotel nights paid for.
I usually stayed either with family/friends or in cheap hotels. The priceline "name your own price feature" worked VERY well and put me in 4 star hotels for the price of a 2 star hotel. We still use it today when we travel.
Couch surfing is not a bad idea, and we initially discussed creating this type of function within interviewSEASON. We moved it to the back-burner because we wanted to focus on other utilities that would benefit the general population first. Obviously couch surfing will save you money, but here are some things to consider this before opting to couch surf the night before the interview:
You will have to deal with somebody you don't know as you're trying to get out the door on the morning of your interview. You'll also have to deal with them and lack of privacy the night before the interview. Even though a hotel room will cost you some money, there are some advantages to having your own room the night before your interview. Couch surfing is probably not so bad if they are medical students who know the situation. I would not use one of the general population couch-surfing sites.
If you are going to try to couch surf with fellow applicants, you could try using the "Residency Match" facebook group to connect. I'm not sure that it would work for what you're looking for, but it might. The ability people will have to see a little more info about the person they're considering putting up (or staying with) may make it easier. You could even start your own "Residency Match Couch Surfer Group" just for people who are interested in couch surfing with each other.
Good call on staying off of the internet.
Best of luck.