My husband and I are planning to spend 3 days (July 25-July 28) in the LA area. What areas around there (beaches, etc) are safest and most economical?

Consider Manhattan Beach, Hermosa Beach and Santa Monica. Santa Monica is probably best if you're planning to drive/tour around L.A., Hollywood etc.

www.bayviewhotel.com
www.seaviewinnatthebeach.com
www.seaspritemotel.com

Santa Monica

tracy has given you great advice. Of the three cities listed, Santa Monica will probably be the most expensive. What is your maximum per-night rate (and remember that you pay sales tax and hotel tax in CA)? If you can stay somewhere removed from the beach, the hotels in Beverly Hills, West Hollywood (properties north of Santa Monica Blvd.) and Westwood might be worth a look.

An important question, given the size of the greater LA area: What do you want to do in those three days?

I would recommend against the Sea Sprite (yet again). If possible, it has gotten progressively worse. See recent tripadvisor reviews.

The Best Western Sunrise in Redondo Beach is reasonable for being that close to the water. There are also economical properties along PCH in Manhattan & Hermosa Beach, such as Holiday Inn Express.

Just off of the 405 freeway, in the Manhattan Beach/El Segundo area, there are lots of suite properties, such as Hawthorn Suites, TownPlace Suites, etc. These often have a small kitchen, and serve a free buffet breakfast. They are about a 5-10 minute drive to the beach, and close to the freeway for visiting other parts of L.A.