Are you staying in a hotel at LAX? Or are you leaving the airport for a few hours just to go into Hollywood (in which case you will have all your luggage with you so I guess that's not possible).
Anyway,
taxi from LAX to Hollywood runs anywhere from $40 to $70 depending on traffic.
There is a coach that goes from LAX to downtown, the UNION STATION FLYAWAY. It picks up at every terminal right outside baggage claim.
From Union Station you can hop the metro subway up to Hollywood. Coach is $4 and takes about 45 min, subway is another $1.25 and takes about 20 min.
Taxi could take anywhere from 30min to an hour. Arrival to the airport at 2pm probably means light traffic on the way to Hollywood if you leave right away. After 3pm it will pick up. And the taxi ride back from hollywood to LAX would be an hour due to heavy traffic until 8pm.
Be sure to ask for a "flat rate" before taking a cab, otherwise they might drive you all over h---.
