Please note, I've only lived in Austin for a few years now, and that's been solely as a poor (and generally car-less) college student. I think a city like Austin deserves a writeup detailing its different areas and maybe giving some kind of feel for the local color, and I'm going to start. I'd love to see other people that live/have lived here add to this and give their own impressions. That said, here goes.
East Austin - Austin's version of a ghetto. East Austin is a broad term for the part of the city east of the freeway and, usually, north of the river. Locals seem to believe that it's really really bad and incredibly dangerous, but in all honesty, it's really just the relatively quiet and lower-middle-class black part of town. There are a few blocks that you really shouldn't walk through after dark, and a few more where you're liable to get your hubcaps stolen, but compared to really bad parts of larger cities, East Austin's practically the suburbs. Historically, East Austin is the artifact of discriminatory housing practices, dating back to the period immediately after the Civil War, and only ending in the 1960s, which kept blacks and Chicanos bottled in the eastern part of town, which was largely allowed to stagnate. It's no coincidence that when I-35 was layed down here, it was put more or less directly on the racial dividing line, creating a de facto wrong side of the tracks. In the bad old days, and to a lesser extent now, East 11th Street was the internal dividing racial line: north of it was the black ghetto, and south was the barrio.
South Austin - South of the river and north of the suburbs lies one of the most interesting and diverse parts of town, and in many areas the most authentic holdover from the pre-Tech Boom era. South Austin is where much of the Chicano population of the city is concentrated, along with a large chunk of students, recent graduates, and miscellaneous other refugees from downtown. The most common bumpersticker found in this part of town reads "Keep Austin Weird!", which is both a celebration of Austin's legendary quirks, and a gauntlet thrown down at the johnny-come-lately North Side yuppies and dot-commies.
- Downtown - The bustling heart of the city. Think expensive restaurants, tall buildings, and serious men in suits. Downtown Austin is like the downtown of any fairly wealthy small city, and the prosperity of the tech boom has only made it more generic. Construction is everywhere, parking totally impossible. With a few exceptions, the downtown area is probably the part of Austin that's least representative of Austin as a unique city.
- Sixth Street - When people talk about Sixth Street, they're usually referring to about eight blocks of East Sixth between Congress Avenue (the centerline of downtown developement and the city's street grid) and Interstate 35. This area is the serious club and bar district in Austin and the focus of a revitalization of downtown which started in the '70s. You can find clubs devoted to more or less any genre of music you've ever heard of, and a few you haven't. On weekends and holidays, Sixth gets rowdy and full of drunk and often obnoxious frat boys and tourists, but on weeknights and when school's not in session things are a bit less frenetic. One thing Sixth Street is almost as famous for as music is corruption - everybody from venue owners to musicians to the cops to random passersby are usually bribing everybody else, and the the blocks immediately around it are full of bail bondsman's and qwik-loan joints, which doesn't really increase the atmosphere of wholesomeness. West Sixth, going about the same distance in the other direction from Congress, is the grown-up version; substitute brewpubs and yuppie bars for the meat-market dance clubs, and just darling little French restaurants for the bail bondsmen's.
- Capitol of Texas and area - The capitol of Texas itself, slightly north of downtown proper, has a slightly fairytale aspect to it from the pink native granite (not limestone, thank vivid for the correction) it's constructed out of. True to Texas form, the capitol dome is six feet higher than the national capitol in Washington. Just because they could. The area around the capitol is surrounded by the acoutrements of state government - the Governor's Mansion, various state executive departments, no-nonsense lunchshops which cater mostly to government sararimen and such, and some of which can be quite good if you just make sure to hit them at anytime other than the lunch rush.
- University of Texas - The University of Texas campus itself isn't terribly different from that of most other large state schools. Of particular interest to non-students might be the University of Texas Clock Tower, symbol of the University and site of the famous Charles Whitman shootings. If you look closely at the grounds around it, you can still see the bullet holes in the walls. Also worth a (brief) look is Jester Center, the largest civillian dormitory in the world, a 4000 person strong human anthill and city-within-a-city.
- The Drag - The chunk of Guadalupe Ave. abutting the west end of the University of Texas campus, full of coffeeshops, used record stores, vintage clothing places, cheap restaurants, and other college town staples. Richard Linkletter's Slacker was filmed here in the early 90s.
- West Campus - What in most college towns is called "Frat Row". There's also a lot of inexpensive housing for independent students here, but the presence of the fraternity and sorority houses sets the general hard-partying tone. The nicest or the worst part of West Campus, depending on your attitude, is that the police will tend to stay out of here for anything short of major civil disturbances or structural fires.
- North Campus - A little nicer and a little more expensive than West Campus. Most of the apartments here are old homes that've been subdivided into smaller units to rent out to students. Because the older buildings haven't been knocked down to put up giant ugly apartment blocks, the neighborhood has a more quaint and picteresque feel, and is one of the nicest areas in the city for walking through.
- Hyde Park - North Campus segues into Hyde Park around 40th Street or so. Hyde Park is one of those mixed-use neighborhoods that urban planners love - multi-ethnic, multi-income. It's also one of the older neighborhoods in the city, with a history dating back to 1890s, when it was founded as a wealthy residential neighborhood; a state of affairs which gentrification is, perhaps ironically, rapidly returning it to. Also notable is a years long zoning squabble between the local residents and a giant Baptist mega-church which owns four or five blocks in the middle of the neighborhood, precipitated by the church's constant expansion, particularly a plan to put up a large and ugly four-story parking garage in the middle of a residential area.
- South Congress and South First - Just south of the river, along these two parallel roads, is an eye-catching neighborhood full of upper-end Mexican restaurants, vintage stores, art galleries, and the like. Colors are bright, the general atmosphere laid back, sometimes to the point of happy catatonia. South Congress is the more self-conciously quirky, see and be seen half, South First the more down to earth, authentic, and reasonably priced half.
- East Riverside - This is where I live. It's about an equal mix of poor students and poor Chicanos. It's basically a long, highway-hugging, cheap-ass bedroom neighborhood, made up mostly of two-story apartment complexes that look like they'd fall over in a strong wind - much of it is either student housing or Section 8. Most weekends, especially when the weather's warm, the entire neighborhood turns into one loud, raucous block party. It's all about the low-rent charm.