What is the nature of your visit if we may ask?
Aside from the ocean stuff.. there's not really much nature to sightsee in busybody LA unless you start going towards the mountains. the Aquarium is as far as it goes for interesting and marine nature things.
You will need transportation if you plan to check out all the wonders and attractions of LA.. Southern california is a land made for automobiles and hostile to all other forms of transportation.
Nightlife is done in local bars (bj's etc), piers (santa monica has the bigger one), 3rd street promenade as a few to name. Daytime people are bustling around doing their job crap.
Then there's the usual LA attractions.. shopping, plaza, movies, town centers, LB has one, but it's a bit up northwest-ish.
To be more detailed on transportation, you can most likely take the metro green line from LAX and then switch to blue to go down to LB depending on where you're staying.
Then for the rest, walking all the way around will be a bit tedious. You can try the local buses and stuff. I don't recommend going too far on them because the bus here is for people who usually don't seem to be able to afford luxuries of life like cars, homes so you'll find some crazies on there.