Number 1 on the must visit - Cabela's.
Make sure to go to the back of the store and then turn left. They have a gallery with some incredible deer mounts. There are more around the hunting and bow areas, but the gallery has the jaw droppers.
There is an interesting aquarium with native Texas fish in the front by the customer service desk.
In the everything else after Cabela's stop:
Guero's for Tex-Mex. For a more upscale Tex-Mex, Manuel's near the Arboretum is very nice and still pretty moderately priced. The Arbor Theater across the parking lot has "art" films if you want to try that - wives can really like that a lot.
Benny's out Hwy 71 about 10 miles east of the airport for BBQ, or make a trip to Lockhart for Black's or Smitty's.
IMO skip Salt Lick. In the times I've been there, it is very crowded, loud, has long waits and is overrated. Driving to Black's or Smitty's in Lockhart will be faster, better BBQ, and a better experience. Benny's is just a little shed on the side of the road with some picnic tables, which is nice a sunny day. Black's has some very impressive mule deer on the wall, which is worth a stop if you are so inclined.
Eddie V's as mentioned. The Arboretum location is nicer and with a bit older crowd. Check online for reservations and music at both locations. Roaring Fork downtown or north is excellent. Make sure to order the macs and cheese with green chilis. I never eat macs and cheese and this stuff is tasty.
Austin Land & Cattle has great steaks and chicken fried steaks. With the legislature in session, it can be crowded with politicians and lobbyists.
If you or your wife like to swim, Barton Springs is a real treat with spring fed water, albeit a bit on the chilly side. Just jump in and start moving. After a minute or two the water is great.
Sienna on 2222 @ 360 is very nice Italian in a beautiful building.
Kerby Lane on Kerby Lane is good for breakfast around the clock. The pancakes are a specialty. Definitely very "Austin" feel to it, or at least the older hippy "Austin" feel to it.
The Bullock Museum usually is interesting if you like Texas history.
For a day trip, the Nimitz Museum in Fredericksburg is interesting for WW2 history.
Warning, women like all of the "cute" shops in Fredericksburg, so lock up the credit card or be prepared to have smelly candles and water buckets with bluebonnets painted on in your house.
The Arboretum and/or Domain are both nice if your wife wants to go shopping.
The South Congress scene and shops are very trendy with all of the hipster crowd which seems to be a hit with the ladies also.
Allen's Boots and/or the bar at Guero's are there for an escape from the "SoCo" scene.
The Stephen F. Austin is another nice historic hotel downtown.