Planning a trip to Sturgis SD in August. A bucket list thing for me. https://www.sturgis.com
Plan A was to rent a car, drive to Sturgis (via Las Vegas as it turns out), staying in cheap motels and pitching a tent at Sturgis and risking the weather. I can fit all my camping kit a my suitcase allowance.
Plan B is to rent an SUV that I can roll out my air mattress and sleeping bag in and free camp. Apparently a lot of casinos, many Walmarts, truck stops allow free camping but you must not get anything out of you car/SUV/RV. All cooking must be done inside, no chairs or tables outside, and nothing dropped on the ground. Some places you can pay $10 for a water topup and a shower. This is called boon-docking so I found out today.
That's Plan A to Plan B. Plans C - Z to come (maybe).
Many years ago - 1970 in fact - I had 4 weeks in the US. I bought a 1960 Chev Station Wagon and drove 7000 miles in that time. I paid $350 for the car and sold it for $250, so it didn't owe me much at all.
I intended to camp in trailer parks etc, and the first country town I came to, I went to the local police station to ask where the trailer park was. They said that there was no trailer park in that town, but I was more than welcome to set up camp at the top end of the town park. I was a bit iffy about this, but there was no alternative. They asked me for my car licence number (which I gave) and they then commented "Thank you Sir, we will not bother you tonight, Have a good sleep". Thereafter, each town I came to I went to the local police station and asked where the trailer park was. Most of them told me the same story - I was better off in the top end of town park. They patrolled the area and once they had my rego number, they would not bother me.
I doubt that this practice is still allowed today, and it was not allowed then in the major cities, but it certainly saved me a lot of money and I also met up with a lot of interesting people (other campers) in each park. As soon as I opened my mouth, it was obvious that I was not a local and in many instances they even shared their dinners with me. Totally different to the attitudes in the cities of course.
Camping in the National Parks was different again. Conditions varied everywhere, but I remember waking up in the morning with about 6 mm of ice INSIDE the car windows. In Yosemite, the park had closed down for the winter, but they allowed me to camp in one area near the showers (cold because everything was shut down). I bought a bucket of about 10 fried chicken pieces (to eat hot and the rest for later on). Whilst chomping away on my third piece, I heard a lot of crashing noises outside the car. I turned on the headlights and there were 3 good sized bears circling the car - they had smelt the hot chicken. I needed to wash up and ablute after the meal, but there was no way I was going to walk to the toilets. I would have smelt like one big chicken drumstick to the bears... I didn't have a shower that night either...
As said above, I doubt that camping would be allowed in the city parks these days, but it may be worth checking up. I certainly met a lot of interesting people in my camps, and the fact that you are not a local I am sure would still open many doors for you. Again, the local police were very helpful with their directions.