Walk, Bike, ACL Shuttle, Uber
Yes, Austin City Limits offers a shuttle from Republic Square in Downtown Austin. The shuttle is free, runs continuously throughout the day, and drops you off right at ACL.
If you are close enough to Zilker Park to walk or bike this would be the easiest way. Some people don't mind walking from Downtown Austin, but it admittedly is a bit of a hike at around 2 miles. By bike it will be a brisk ride, but walking it is a bit of a trek but many people do it. If you don't want to walk or bike I really enjoy using the official ACL Shuttle. It picks up at 5th & Guadalupe, just a few minutes walk from Congress Street, so it will be convenient for almost anyone. The bus runs continuously throughout the day and usually has a pretty short line to board. Some caveats are half the buses are nice coaches with AC, and some are old, crappy school buses. It really is luck of the draw with what you get, but one can’t complain too much with a free shuttle. The shuttle takes you back to Downtown Austin at the end of the day as well, dropping off right where it picked up. Note that the line to board the bus at the end of the night can get annoyingly long, especially if you go
Free if you walk or take the shuttle. If you go with a bike you can use the Austin Bike Share program B-Cycle for $12 a day.
No, there is absolutely no parking available at Zilker Park, where Austin City Limits takes place.