A bar like Rio Rita
Try Fino for cocktails - one of the best bar chefs in town. Malverde also slings some great cocktails within a truly beautiful bar setting. If it's not open - you can drink from the same menu downstairs at La Condesa - an upscale, contemporary interior Mexican restaurant with excellent food. Neither are cheap - but both are worth the price.
400-A W 2nd St, Austin, TX 78701
Staying on the East Side- you could try Shangri-La, the Liberty Bar, Longbranch - they all have similar vibes to Rio-Rita. Cocktails will indeed be better at the Good Knight, and if your pretentious tolerance is high - the steampunk flair of the East Side Showroom can also be fun, but not cheap. And Cheer Up Charlie down the block is beer and wine only, and even more of hole in the wall - well a glorified trailer to be exact - than Rio Rita, but sometimes wild dancing in the back! I miss the Peacock Lounge.
Some other unique Austin drinking establishments in my book would be the Dry Dock on Mt.Bonnell Road- beer only, and falling down, but fabulous views and good old hippy Austin atmosphere. Peche makes fabulous cocktails but is a tad yuppy. My favorite country bar remains The Broken Spoke on south Lamar. The patio at Club de Ville under the limestone cliff is also pretty cool, and the Hendricks rosemary cucumber martini at Parkside is one of my favorite drinks in Austin. A mojito on the patio of Red House on Manor can also be a jolly event. Now you've got me wishing my life away till happy hour.
3201 S Lamar Blvd, Austin, TX 78704
1917 Manor Rd, Austin, TX 78722
208 W 4th Street, Austin, TX 07739
The chief bartender at the Good Knight can mix pretty much anything, including rum drinks. He consistently makes some of the best and most creative cocktails in town. On the down side, you certainly will pay for the privilege of drinking one of them! Rio Rita and Good Knight are owned by the same people, and they are clearly intended for different markets and different wallets.
If you're dead-set on going to a bar that doesn't feel like others in town, you might try the Draught House, which has a reasonable selection of brewed-on-the-premises beers, and has a very cozy, neighborhood-pub feel. Gets pretty crowded at happy hour times, but I feel that speaks well for the place.