Ozjet, stay in Santa Monica at the Shangri La Hotel (
http://www.shangrila-hotel.com) which has big rooms, is quite inexpensive for LA, has kitchens attached and is on Ocean Avenue facing Santa Monica beach but two blocks from the promenade where you can eat easily any time of the day. Oh yes and they give you brakfast and afternoon tea. Santa Monica by the way is perfectly safe and will give you an idea of the famed laid back Southern California sunshine thing.
You need a car. Otherwise forget LA. Just not possible and not worth being here. Book Hertz. Collect at airport. Time to Santa Monica, 30 minutes. Go down Lincoln Boulevard.
When you get the car you drive on the 10 freeway from Santa Monica to the 5 freeway, head south and arrive in Disneyland. Total time 50 minutes to an hour and a half. Coming back 50 minutes. Universal its the 10 freeway to the 110 North to the 101 North. Drive time, 40 minutes to an hour. Coming back same thing. That give you two other days to see Beverly Hills, the Westside generally, Getty Museum, Malibu or just cruise around doing whatever.
I had someone in town doing what you're doing last week. Perfect time and reasonable combination of chill out and running around.