When I was a teenager and a little older, hitch hiking around, I always traveled with a back pack. Usually, I could catch a few Zs during rides. If I was out in the country, I could set up camp in a secluded spot. I had a small nylon pup tent and a light sleeping bag. In big cities, if you asked around, there was usually a youth shelter you could go to for free in the basement of a church somewhere. During the Summer, College dormitories would put you up for a dollar or two, that was a great deal. If I was staying someplace for a while, I would look for a situation where I could get a place to stay, for free. It's not that hard and when you're young and traveling around, you have time to do it.
Once I got a little older, life got a little more complicated and I had a few obligations, especially related to time. I had to pay for rooms. There were cheap hostels around and YMCA hotels. They were clean and friendly. If they weren't available I would look for an old, large, commercial hotel in the bad part of town. These are the kind of places where the rooms are the size of closets. They have a single bed, a chair, and if you're lucky, a wash basin that you never want to use for anything other than a urinal. Toilets and showers are at the end of the hall. They don't necessarily change the sheets between guests. You ask for a towel. It costs extra and you leave a deposit. They rent rooms by the day, week or month. They have vermin. It's OK, they don't hurt you. You never leave anything in the room when you're not there. When you check in, you let them tell you the price, then tell them you need the sailor's discount. They'll cut the price in half, sometimes more. There was a place in San Francisco, the Apex Hotel, in the tenderloin, where I liked to stay in the late Seventies. Cheap hotel/motel rooms went for $8-$12 then. They charged me $2. Inflation was horrible then. Once they knew me, they never raised the price.
I'm sure there are still places where young travelers can stay for cheap, even for free, if they use a little initiative. The World never really changes. I do though. I'm old now. Big difference. I book ahead on the internet. I use sites like Hotwire and Priceline. The cheapest rooms I can usually wrangle anywhere, are in the $30-$40 dollar range. They are very basic but OK. For a few dollars more and I really mean just a few, I can get a much nicer room, in a nearly luxury establishment. I usually shell out for that. Why not, I've got the money, at least today I do. I like San Francisco. I can usually get very nice rooms there for $45-$55 dollars. If you book these same places on retail sites like Expedia or Orbitz, they charge $100 minimum. A lot of times it's $30-$40 more. If you walk up to the desk with your suitcase in hand, fagidaboudit.
The best deal I ever got, was for a friend of mine. Last spring she spent a week in NYC. She and her husband were going to share a room at the YMCA, bathroom down the hall, at $120 a night. I got her a top floor, concierge service room, at the new midtown Wyndham Garden, two blocks from Penn Station, $75 a night for the whole week, on Priceline. Retail sites were quoting around $200. The desk was quoting $325 then and this Summer, $500 for a standard room. She owes me. She also now thinks I'm some kind of intertube genius. I'm just cheap.