1) GET PERMISSION
I can't believe that I need to state that, but you would be surprised. Most parks explicitly state that they are closed after dark. It sucks being woken up by the police at 2am. It sucks having parents think you're a potential pedophile or something. If the notes on the Adventure Cycling map says "check in first with police", check in with the police. It not only makes what you're doing legal, it shows courtesy on the part of cyclists. I have met cyclists in Kansas who had not once checked in with the local authorities since leaving Boston. My only exception to this rule is if 2 or more townspeople tell you "Oh, it's just fine to camp in the park, honey."
2) SELECT YOUR TENTSITE
In the above photo, you will note that I am camped on dead grass. "What a jerk," you're thinking. "He's just gonna kill the grass further." There's a reason there is dead grass and lush green grass: automatic lawn sprinklers. I lost count of the number of cyclists who recounted being woken up in the wee hours by a sprinkler shooting water in through an open tent door.
Of course if there is a pavilion, then you're set. Just don't yardsale your stuff all over the place. Citizens of the town may want to use their park as well. This saves you the hassle of setting up your tent. Sometimes conditions warrant setting up the body of your tent anyway. Like the time I saw a skunk moseying around the pavilion at twilight.
3) CHECK THE BATHROOM
Is there a bathroom? Is it unlocked? Did you check in with the police who will gladly unlock it for you? Is there toilet paper? These are all important things to reconnoiter before you should need to utilize the facilities. I travel with a spare supply of toilet paper just in case. Which reminds me- Is it general practice in Mexico to provide your own toilet paper? The first few days of travelling there I found myself being rather inventive til I caught on...
Sometimes you will luck out and there will be a shower at the park. Many times if there is a public pool, you can go up to the counter and the teenage girls running the joint will take pity on your state and let you shower for free. Check in at volunteer fire departments too. Or just forgo a shower. The clerk at the 7-Eleven wasn't buying any of your pickup lines anyway.
4) FIND A WATER SOURCE
Is there a water source around? Are you capable of actually filling a water bottle from this source? Don't laugh. If you only have tall 24oz bike bottles, you may encounter water fountains or faucets that completely foil you.
5) GET SOME POWER
Now that you scored a free shower, you probably want to break out your hair dryer and do some styling. Or you need to charge up your iPod so that you can listen to Kenny Loggin's Danger Zone on repeat tomorrow as you mindlessly drift through Kansas. The best place to find some power outlets would be around a pavilion or inside a bathroom. 2% of the time the power will actually be turned on.
6) HANG YOUR FOOD
If there is any possibility of critters getting in your food or a bear being attracted, make some attempt at hanging your food out of reach. Much of the time you can easily clip it to a pavilion beam or sit it on top of a bathroom roof but you may want to carry some cord if you need to hang food from trees. Locals will assure you that there is no need to do anything with your food. You will acquiesce because you're tired from a long day of riding. You will meet the resident raccoon that is the size of a German shepherd that's opening your panniers the hard way.
7) OTHER STUFF TO STAY AWAY FROM
Do not camp anywhere near a ballfield. Ever. It may be late and you'll think, "No one could possibly start a game this late." They will. You will believe that you have been transported to Williamsport, PA for the evening- the home of the Little League World Series. They will turn on the spotlights that transform night into day. There will be an announcer. You will not sleep.
Stay away from standing water. Standing water breeds mosquitoes. Despite my best efforts, last night the mosquitoes were tapping so furiously against my tent fly that it sounded like it was lightly raining outside. If you camp at the Mormon historic site in Sweetwater Station, WY you needn't worry though. They run around camp on an ATV with an industrial mosquito fogger on it at 6am. I wish I were kidding.
Stay away from the playset. Believe it or not, there are parents that will allow their children to play unattended well after dark. It may not matter. One night in Ellington, MO I had kids concealing themselves behind my tent during a raucous game of Hide and Seek. If any parents are chaperoning their kids while you set your tent up next to the playset, they may mistake you for a vagrant and then call the police who you forgot to check in with earlier.
Stay away from the swings. Unless you really want to hear two 14 year old girls describe just how much they hate their parents and learn why Johnny Cooper is the cutest boy in school. Then lie back and relax. It's sort of like a juvenile podcast I guess.
8) BE RESPECTFUL
Treat everyone that you meet with respect. The townspeople are the ones paying local taxes that keep the park open and the water turned on. It is by their good graces that they allow you to camp there. Clean up all trash, even if it isn't your own. Close doors and gates. Don't make a lot of noise where there are nearby houses. Think of it this way: if you weren't riding a bicycle and doing something that they think is awesome, the local police would lock you up for being a homeless bum and parents would pepper spray you for saying hello to their kids. Don't screw it up for the rest of us.
Hopefully you have found this short guide to be helpful for camping in parks along your bicycle journey. It's typically the cheapest legal way to spend the night and affords you the opportunity to meet new folks all of the time. Also, a community welcoming strangers into their park in order to fulfill that cyclist's dream of riding cross country truly warms my soul. In an age where we are conditioned to fear one another and be shocked and awed by the news every morning, it's nice to see regular folks helping one another out.