The main sights of LA are ridiculously spread out so as convenient as Anaheim is for Disneyland, it's not for other tourist attractions so you don't 'have' to stay there. If you're only going to go to Disneyland, then yes, it would make sense but if you plan on seeing the other major sights, you can broaden your search.

We stayed in a backpackers in West Hollywood on our first trip to LA (when we also went to Disneyland) and location wise it seemed pretty good. We got transfers from our hostel to Disneyland and back and we spent a whole day there, about 12 hours straight at the park. It was perfectly fine for us (we were in our mid 20's then) but not so great for little kids. If you were planning on doing multiple days there, you'd probably want to stay very close by as the transport to and from could get expensive and time consuming due to the horrendous traffic (I'd recommend transfers or taxis as the public transport is pretty ordinary).

West Hollywood seemed to be quite handy to visit all the major Hollywood attractions, Beverly Hills and Venice Beach. It wasn't too far to Universal Studios either (well worth a visit!)

The second time we went to LA, a few years ago, we stayed at a nice, small hotel in Beverly Hills. We were walking distance to Rodeo Drive which was nice and a short taxi ride to the Sunset Strip. It wasn't too bad price wise and once again, we weren't too far from several major attractions. We even caught public transport to Santa Monica which was time consuming but easy from Beverly Hills. We did a day trip to the Queen Mary at Long Beach and got private transfers to and from it as recommended by the hotel concierge. It would have taken us a good couple of hours or more on public transport and several bus/train changes too apparently. As it was, it took us a good 45-60 minutes by car and that was direct!

Hope some of that helps.