Ok so camping in a city park or walmart parking lot is not what I really consider camping, but sometimes you just need a break from the road and a city park may just fit the bill for a overnight or for 2 or 3 days.
Here are some city parks with 3 day free camping.
These are all in Texas so they are camper friendly there, not all states are. The parks are top to bottom.
Waylon Jennings Park in Littlefield TX
Coleman Park in Brownfield TX
Levelland City Park in Levelland TX
I will post more city parks like this until I can make pages for each state.