It is very difficult to tailgate there due to the parking situation ("stacked" parking as I saw someone else mention). There are picnic tables just outside of the bowl, and I've kicked back there and ate/drink without problems.
I'm doing the park and ride from Lakewood; there's also a shuttle bus available (check out the hollywood bowl website). These are the best options to get there in time for the show, as traffic will be horrid.
Have a great show.