There is a ton to do in Austin, even without a car. Unless you are up in Cedar Park or Round Rock or some other suburban hellhole. If you are anywhere centrally located the bus can take you most anywhere. Everything to do in Austin during March is centrally located.
Edit: Quick list...Zilker Park, canoeing Town Lake (or paddle boarding if you like wasting money), walking/jogging Town Lake, 6th street all weekend, Continental Club for music, Ephriam Owens playing Jazz at the Elephant Room, eat anytime between 10p-6a at Magnolia Cafe on Congress, get the beef fajitas at Polvos, get the chicken mole at El Chile, grab a beer and a burger at Hopdoddy's, get pizza or just a slice at Home Slice, if the sun stays out like it has been today (reasonable) then Barton Springs Pool would be nice to lay out at.