Hostel California

on http://www.hostelsweb.com/cities/losangeles.html you can find several hostels in the Hollywood area:

USA Hostels Hollywood,
Orange Drive Manor Hostel,
Hollywood International Hostel,

I do not know anything about these places, other than their locations are in the middle of where your Hollywood expectations probably are: Hollywood Blvd between Highland and Vine. Hollywood can be shady after dark, so if you stay in Hollywood, do be careful of your surroundings, and look for security features in the hostels.

A "good" location can mean convenient, and these are certainly. It can also mean well-to-do, expensive, safe, boring, and Hollywood is not.

As for the beach side, Santa Monica, Venice are certainly good/desirable destinations, Venice perhaps more eccentric and bohemian, while Santa Monica is more upscale. There are several hostels in Venice beach listed in the above web site.

http://www.lahostels.org/ has hostels in Santa Monica. Personally I would prefer to stay in Santa Monica, and go to Hollywood for all the sight-seeing you want to do there but would not stay there. (however, I am not a backpacking young person, so take my view with your discretion) Santa Monica is just north of Venice, and the beaches there is a good starting point for more beaches north like Malibu and south like Manhattan Beach or Torrance.

An alternative to hostels is to try couchsurfing, a way to stay with a local person, it just sounds like a wonderful idea. Check out couchsurfing.com and Amanda's review about what it is http://www.travbuddy.com/Couchsurfing-v5754