The Huntington is a beautiful botanical garden with diverse exhibits. Definitely recommend for a peaceful few hours!
Griffith park has countless hiking trails to explore, and you can drive to the top if you want to check out the observatory! (of La La Land fame)
This is a challenging out-and-back hike, but it's one of our absolute favorites! You'll get beautiful expansive views the whole way. There are many more trails in the Angeles National Forest if you're looking for something different.
Old Town Pasadena (primarily along Colorado Blvd) has lots of shopping and restaurant options!