If it's your honeymoon and you want to have a DECENT place to stay, you'll need to 'up' your budget. Los Angeles is expensive. You're spending thousands of dollars to fly here; what's another $200 for a hotel? If you can't afford it, drop the car. As Yoga said, you can reach Hollywood and Universal by public transit (or on foot) if you stay in Hollywood.
For your dates, I'd look at these hotels:
1. The Hollywood Hotel -- this is the only 3-star hotel that will be affordable:
It's to the east of central Hollywood (10 minutes by car or public transit). Getaroom.com has rooms for $131 / night plus taxes. Parking is $20 per day. The rate includes breakfast. There's a pool and Jacuzzi on the premises.
2. The Hollywood Hills Hotel on Spaulding Av (not to be mistaken with Best Western Hollywood Hills Hotel on Franklin Av). This is an older 2-star hotel in a GREAT CENTRAL location in Hollywood on a hill overlooking the city just above the Magic Castle Hotel (you check in at the Magic Castle Hotel since they own both). The pool area of the hotel has sweeping views of the city. Rooms are available for $149 + taxes through cheaptickets.com. Their website shows ONE ROOM left (with a king bed).
I would not wait to book!