You could try the nearest Wal-Mart, they allow overnight parking.

A lot of cities issue one-day permits for moving trucks. Go to your local police station and ask if you can buy a permit.

You could call U-Haul and ask if you can park it on their lot.

All good suggestions above. If you have a motel nearby they may allow you to park for a small fee, or you might get away with parking there and them not noticing you are not staying there if it is a busy lot.

Depending on the size of the city you live in, especially large gas stations might have large parking lots for 18-wheelers to camp out. Over-the-road truckers can only drive a specific number of hours in a row, so gas stations that accommodate them frequently have areas for the drivers to park their trucks and sleep in the cab. I’ve overnighted in these before, it was never a problem. Then again, it was on a long roadtrip through sparsely populated areas (i.e. Wyoming, South Dakota).