Have you already booked your trip?
The closest hotel to zilker is probably the Hyatt. Either way you'll probably want to take one of the free shuttles to ACL, it definitely is not walking distance.
See if you can find where the free shuttle pick up is this year. usually it is at 4th and guadalupe at republic square park. If you do that, then that opens lots of hotel options downtown - Hilton Garden Inn, Marriott, W, etc
I've stayed at the holiday inn before. It's average. There's definitely nicer hotels plus the holiday inn is a hike to downtown.
Uber and Lyft are in Austin but during big weekends like ACL the rates are $$$ Taxi's are hard to find.