Don't know where, etc, but if thinking of super cheap, you MAY still find yourself better served at a very inexpensive motel, a hostel, or other facility. At least you'll have some security, so to speak, or peace of mind. I would not encourage living out of your car.
By the time you spend a few bucks for a shower, and gas to-from, you're probably close to $7-10.00 per day. Add the discomfort of sleeping in the car, even in a "safe" place, the uncomfortable and lack of bathroom facilities, and more, much more, you may find spending a few bucks more well worth the expense.
I'm thinking you should be able to find some place to stay in the very low $20's or less. Especially if you check online (Craig's List, Back Page, etc), and search for cheap housing like hostels, perhaps dormitories, etc.
It's been awhile since I've traveled that cheap, but in 2009 I spent an average of $19.xx per night over 50+ nights in Vegas, at "real" hotels. When I used to regularly visit Biloxi, I was paying $80-$100 / week (depending of events in town, etc), 7-10 miles from the casino strip, in a run down motel owned by mom & pop. But I only needed a place to sleep and shower, and that was pretty darn affordable. I could get a better price if I did not want the weekends. LOL btw: some of those places can be pretty filthy, and you do not want to park a nice, current model car at some of them.
Over the years, I've probably slept overnight in my car well over 100 times to save money. Also, it used to be, that you could check into a cheap motel after 7 am 'ish, and keep the room close to 30 hours. (More if you ask for a late check out later that day from a different desk clerk than the one who checked you in.) I did that more times than I can remember, sleeping twice for the price of one night. Again, it's been a lot of years since I've done that.
I used to travel a lot for work, and often had a per diem expense account for lodging and food. When I did, I'd do whatever I could to use less. MUCH less.
Oh, yeah. Another source for showers..... the YMCA