As a slumlord, I'd say rents are high in central Austin, but with all the new buildings, I'd look into the older complexes, especially if they are next to the new high rises. The one catch about living off campus is that leases are generally 12 month leases.
Riverside has been built up and hardly looks like it did back in the day. But again, there are older complexes, probably new in the 80's when I lived out there, that can be a little cheaper rent wise.
With 2 kids, you can look at buying a condo. Your girls can get a friend or two to room with them to offset the costs. Only thing is property taxes will be astronomical. Watch out for HOA fees too if you buy. Don't kid yourself, if you rent, you are paying for that. It may be cheaper to buy if you are looking at 4 to 5 years.
Good luck.