There are not many places to live in Austin where you can walk to everything. However, there are some neighborhoods that offer a decent balance. I am not sure if you are looking for a house, apartment, condo or duplex, so I will just suggest some neighborhoods and their surroundings.
SoCo (South Congress) area:
Trendy, upbeat neighborhood with lots of shops, eateries, salons and bars. One local corner market that has enough items. A not too far walk to the HEB (major food store). Accessibility to downtown area via foot, bus or taxi. One local, alternative movie rental place. Rent can range anywhere from $900 to $1500, depending house size and location to South Congress Avenue. Good for job locations south of downtown.
Clarksville (West Lynn and 6th St.)
A mix of yuppie and hippie w/ lots of trend. Great eateries such as Potabla and Chippolena. Walking range to trendy shops, salons, record store, video rental, gym and Whole Foods. Walk, bus, or taxi to warehouse district and 6th street. Rent can range anywhere from $1000 to $1600, depending on duplex, condo, apt or house. Balance between jobs north or south of downtown.
Hyde Park (north of UT campus)
Yuppie and student mixed neighbor with college town feel. Decent eateries, shops and amenities within walking distance. Closest large grocery store is Central Market (similar to Whole Foods). Good location for jobs north of downtown.
Beyond these neighborhoods, there are not many others that allow you the freedom to walk to most of your amenities. Peronally, I live in the Hyde Park area. It is far enough away from Downtown, but still accessible to it. I have lived in SoCo before it was the trendy place to be. I do not care much for it these days, but it depends on your taste. I have friends in the Clarksville area who never want to leave. I could suggest some of the downtown apts or lofts, but the rental price is beyond belief. I hope this helps.