I grew up in Hermosa. In PV, check out Point Vicente light house for a nice walk along the cliffs with gorgeous views of the Bay (and free!). There is also public beach access at Trump National Golf Course in PV, which can take you down to the beach (also free!). One of my favorite things to do when I'm home is grab food at El Burrito Junior (on PCH in Redondo - a tiny little shack with excellent cheap Mexican food), and then walk the two blocks to the beach for a picnic. You might want to rent bikes and spend a day biking along the strand up to Venice or Santa Monica. It's flat and easy, and a great way to see the coast, and better than bussing, I assure you. Public transport is not LA's strong suit, though it is doable. Though you can easily take the metro line to downtown/china town/Olvera street/3rd street Market.
To give you an example of how much time things take, allow me to describe what I did with a friend who was visiting one weekend not too long ago. In the morning we got moving early and drove to the Getty. We saw some exhibits and took a garden tour (the views of the LA basin are incredible). Then we had Turkish food in Westwood for lunch, and went to the Tarpits in the afternoon, and walked around the whole LACMA/Page museum area, which is large and cool. That night we caught a show at the Largo (small venue with affordable tickets and great music/comedy acts), and grabbed a late dinner at Canters, which is a very old school LA diner. The next day we went to China town for dim sum, and then walked around down town and saw union station, the Bradbury building, the 3rd street market, etc. That afternoon we went back to the coast and spent some time walking around Hermosa pier/strand area. It was an excellent tour of LA in two days. You'll have a blast.