What should I be aware of before a road trip?

I have wanted to go on a road trip for a while, just driving off to nearby towns in my hatchback and exploring. I'd start small, like a day or three. The main thing holding me back is uncertainty of what to bring and how to do it, amongst other issues. I think I can figure out the food and sleep, but I was wondering:

• Where to access showers?
• Where to refill water?
• Is it worth bringing a tent (could I set it up outside of a campsite)?
• Where can I park when I need to sleep (that I won't get in trouble for)?
• Am I missing anything else?

Was hoping some of you might have advice. I don't have a whole lot of good people to go to about this IRL.

Edit: Just wanted to say thanks for taking the time to respond!