Of course, the OP's need for input on this subject has passed, but I wanted to respond in case someone else should stumble on this thread with the same question.
I have slept in my car on several occasions:
A single time, I slept in the backseat of my car on a random LA (Studio City) street (parallel parked as previously suggested by someone). In this case, it was an unforeseen necessity, so it was just myself curled up in a ball without blankets or anything. It was the middle of the night, and I scoped out a relatively safe-looking place to park my car and prayed for the best, with the intention of heading out at a semi-decent hour of the morning so as not to risk being discovered by passersby. This worked out fine.
The following occasions were on drives between Dallas and Chicago, which is supposed to be about 16 hours if driven straight through, but I was never able to make it the whole way without endangering my life from exhaustion, forcing me to stop and "nap". During these instances, I figured the best way to remain safe was to park in the parking lot of a motel (I stuck to the "higher end" chains such as Hampton Inn or renovated/new structure Holiday Inns) and also tried to make an educated assessment about the safety of surrounding area. I would stop in the middle of the night, so at those hours, the parking lots are rather full with hotel guests' vehicles. Not to mention, most who are going to check-in to the particular property are probably in for the night, so that lessens the chances of people walking about. The car I drove for these trips was a mid-size sedan with very dark tinted windows, which helped for concealing myself. Unless someone made a grand effort to press their face to the back windows would they spot me. Along with the extra precaution of placing the sun visor on the windshield, I felt overall secure. I made those drives during winter months, so I also traveled with a large, bulky (and VERY warm) fleece blanket, which further helped to conceal me while sleeping in the backseat and I didn't have to worry about freezing to death.
I should note that, although I did consider rest stops for stopping and sleeping, but felt it would make me an easy target considering the possible higher level of traffic.
So there you have it - my own personal suggestions for sleeping in your car.