Why mess with Wednesday morning traffic? You will be taking the 405 South to LAX and a lot of commuters take that as well including many business travelers heading to the airport. Get a late check out, if you can, at your Universal City hotel and go to your LAX hotel whenever you want to Tuesday night. LAX hotels have some of the best values in the city. Make sure it is one nearby (some are miles away but call themselves LAX), with shuttle and a free breakfast is nice. Good thing with Embassy Suites is they offer some complimentary hot items to everyone for breakfast. A cab will probably be more than $50 and take at least 45 minutes, maybe more, to go 20 miles. The Hilton's hotel towncar is $85. Super Shuttle is $18 per person and they will make a number of other stops before LAX.