How is the parking, and were would I find a close parking lot?

There is tons of parking. The main lot should be right under the Tower. Sign says Tower Parking. Enjoy

There is a parking lot at the location. It's $8 on weekdays and $11 on weekends.

There is a garage a few blocks away and a lot for the museum next door. I'm not sure the cost though. We walked from our hotel since we had already paid for parking there.