The L.A. area is huge and includes everything from beach to mountains. You need to hit the tourist spots like Venice Beach and Hollywood because that's part of what makes that area unique. I would rent a car and take a day drive up Hwy 1 and past Santa Barbara. You could head out early in the morning and make your way back that night and see some really pretty scenery.
I would head up into the mountains too (Lake Arrowhead is right there) and maybe even head down to Palm Springs (Palms to Pines is a great road that starts in the pine trees and ends up in Palm Springs. That can be done in a day and gives you another perspective of the area. SoCal is such a varied place and it isn't all beach (although it can be if you want it to be).
There's a lot of variation in gyms and even amongst the chains. If you know where you're staying we could probably give you specific examples of where to try.