I wouldn't stay in Hollywood. Most of it is an expensive dump (but fun to visit!)
In Santa Monica, you're going to be paying premium prices. If you want to be in that area, I'd look in Venice, Mar Vista, Culver City (although parts of CC can be rough)
Pasadena is nice, but it is actually a distance out of Los Angeles. I worked in Pasadena and lived in Venice, and it would take 2+ hours to get home on a bad day. I'd save Pasadena for a day trip and stay further west, especially if you want to spend time in the typical touristy places (Hollywood, Venice, Malibu, Beverly Hills, Santa Monica). Anywhere you're looking to stay I'd check out the neighborhood in Google Maps.
AirBnB rules are changing in some areas where you have to do a 30 day rental. Burbank would be great to stay, but falls under that rule. In the San Fernando Valley, Studio City, Sherman Oaks or Valley Village are nice options that are pretty close to central destinations but without the cost.
What I might suggest is staying two places. I'd do somewhere in central or northern Los Angeles, then maybe a week near the beach. If you're into beach culture (shops, restaurants, people watching), you could easily spend days just beach hopping. DH and I did that recently spending 2 days on the PCH from Long Beach down to San Clemente (stopping where it looked interesting - places like Huntington, Newport, Seal, Laguna, Dana Point), and it was a blast. You could do the same thing on Pacific Ave/PCH from Marina Del Rey up to Malibu or beyond, also. Every beach town has their own feel, and the LA beach culture is very different from OC.
Someone else mentioned with traffic - you definitely want to compartmentalize your visits to certain areas or else you'll lose half your days to travel. Don't try to do Malibu and Hollywood in the same day, for example. Metro is great, but bus travel is not (downtown to the Getty took tourist friends 6 hours!)
Really, for three weeks, you might want to take 2-3 days and go up to Santa Barbara and down to San Diego. The drive up the Big Sur is amazing (and Monterey/Carmel is great), so you could spend a few days and do that as a side trip. I would totally recommend that, cause LA can be exhausting if you're not used to big cities and crowds.