Forget hickory, just steak
Did you see these older threads on where to get a good steak?
My own experience at III Forks was not at all positive [details can be found by clicking on first link, above]. Like tom in austin, I'm a big fan of Backstage Steakhouse.
Of all the steaks I've tried in town, I have to give the best of nod to III Forks. It doesn't reek Austin, but it does reek steakhouse and Texas. And, it simply has the best beef I've tasted around town. You pay for it, it's more like Dallas than Austin, and they have some gimmicks like the line up of servers to give you your sides, but based purely on the steaks they are darn good. Filets are flavorful, but the strips,ribeye, and porterhouse obviously are even moreso. I'd stay away from the "toppings" on the steaks - like blue cheese - because the meat is that good on its own.
I agree with the Tom in Austin about Vespaio also being a very good option for steaks and all grilled meats and much more of an Austin feel. Out side of town, Hudson's beef is very good and one of the less tricked out with sauces dishes on the menu usually and that place is very much Austin.
And of course if reeking Austin (at least old school Austin) is more important than the steak, go the opposite direction and move one step closer to a bipass and go to the Hauffbrau on 6th.
The 12th and Lamar place is Austin Land & Cattle -- which is not a chain and is completely unrelated to Texas Land & Cattle. This place used to be very good. The last several visits I have made have been lackluster.
The best steak I've had in Austin isn't in Austin. Backstage Steakhouse in Spicewood's porterhouse really impressed.
Within Austin's city limits, Austin's best steaks aren't at traditional steakhouses, per se.
While not a steakhouse, Mars (now on South Congress) offers my favorite beef tenderloin. The beef is pretty good, and they cook to order with moderate skill, but the preparation is fantastic: ask for extra sauce, extra mushrooms, and extra leeks. Beef tenderloin (which is very lean) lives or dies by the preparation. Their masterful sauce is the key. Disclaimer: I haven't had the SoCo Mars variant, only the original Mars variant. Depending on what has occurred with the staff, these may be wildly different things.
I can also recommend the steaks at Vespaio. Their oak-fired grill will imbue fatty steaks with a heavenly flavor. Check the specials first -- some might not even be listed, ask! -- and barring that, give their hanger steak a shot (an underappreciated cut of beef -- not bad!). I've had wagyu steak here that was pretty darn good, and a ribeye (on top of a plate of gnocchi) on special that completely floored me.
While the cut of beef mightn't blow your mind, the authentic French prep at Chez Nous rarely fails to hit my craving dead-on. Precede your steak with a masterful salade lyonnaise, the best in town. Note: you must specifically request lardons, and if the waiter is confused, just say "ask the kitchen for lardons uhhh bacon" -- the kitchen knows what to do when they get this request.
Best of luck!