Yes, South Congress is a good place for shopping and eating. Great funky eclectic shops. Everything is in one centralized area and easy to walk to.
Here is a guide to the SoCo area and surrounding area....
http://www.austinchronicle.com/gyrobase/Guides/SoCo
There is an area called 2nd Street District that is in downtown Austin. It is a little up and coming area that has shops and restaurants. The shops are a little pricey (Design Within Reach is an example)... but there are some really great local shops to window shop in if nothing else.
The things that you want to do (rodeo, trail riding) are really outside of Austin like the other poster mentioned. Outside of Austin is really pretty especially going west (the Hill Country). There is a very Texas-y state park called Pedernales State Park about an hour from Austin that has some great little hikes. About 45mins from Austin is Hamilton Pools. It is this super-pretty green swimming hole. Water falls from the top down into the grotto. You can also hike over to the river in the opposite direction. There are probably some horse riding outfits out that way. I don't know alot about that so you might just want to do a google search for it. Maybe someone on here might know about horse riding.
If you want to do some outdoor activities in Austin you can walk/run/bike the trail around Lady Bird Lake (which is great for people and dog watching :) ), rent a canoe on LadyBird, and hike to the top of Mt. Bonnel. There is a botanical garden here that is pretty good (but I'm not sure what it will look like in October... it might look kind of wilted..but it has nice trails for just getting outside). If you like gardens there are two garden shops I really love to visit.... Gardens and Big Red Sun. They specialize in local plants such as cactus. http://www.bigredsun.com/cd_portfolio/show/show.html
http://www.gardens-austin.com/index.html
What type of shopping are you looking to do? I can give you some recommendations. I love to shop (and window shop!).
One of the favorite things Austinites love to do (in my opinion) is to go to a restaurant with a nice patio and sip margaritas and eat Tex Mex (or any other delicious meal). Check out the restaurants on Barton Springs .... there are some nice patios there. The weather will be nice when you come most likely.
..And the other thing we love to do is go to see/listen to some music. Check out the Austin Chronicle for that. There are just too many venues and bands! If you let us know what kind of music you like we can let you know where to go. But for an authentic Texas honky tonk experience you must visit the Broken Spoke. It is this wonky crooked old building that has great old-style country Texas music and couples aged 20 to 80 years old get out and waltz around the floor. If you go on a night with a popular band and lots of people, you will definitely experience something truly Texan. http://www.brokenspokeaustintx.com/
That is enough for now. Have fun in Austin!
Jen