Hi Chris, at which Hyatt Regency will you be staying? If it's the Hyatt Regency Century Plaza, definitely KEEP YOUR CAR. Public transportation in L.A. is sorely lacking in general and in that part of town (the Westside) in particular. Also unlike in most other major cities, we don't really use taxicabs here, so you'll definitely need to hang onto your car in order to get around.

I presume you're flying LAX-London on Friday the 11th? On a Friday afternoon traffic here is particularly bad, I would say leave for LAX no later than 17:00 (5 PM as us Yanks call it) for a 21:15 flight, allowing for traffic, filling up the rental car with fuel, shuttle bus to TBIT, etc.

Have a wonderful time here in L.A., and enjoy the great weather!