I really like the San Diego Zoo, but you might also want to consider the San Diego Zoo Safari Park. Its enclosures are much more vast and open. You can take a tram around a really large field exhibit that some of the African wildlife inhabit together. Note that it is a separately ticketed, separately located attraction.
If you want a more up-close view of the Hollywood sign, there are a few trails in Griffith Park where you can hike very close to it.
As noted, USH is much smaller than UO and thus you'll need a lot less time there. A day for the attractions would be plenty. A big chunk of time will just be spent taking the escalators up and down the upper and lower lots! The same would be true for HHN there. I would definitely use crowd calendars as a guide, but I attended there in 2014 and bought express passes. We walked every house in a few hours. Although I do think it has gotten more popular with the opening of Potter, and that has possibly translated to HHN. On the plus side, it's cheaper!