I've lived in Austin since I was three, so I might be able to help you out on this one.
As for #1:
What age are you and your husband? I'm going to take a stab and guess that you do not have kids. If you do, let me know, because that will make education an issue (lots of wonderful neighborhoods in Austin with less-than-stellar schools). You basically can't go wrong with the neighborhoods just south of downtown and a little bit north of campus. South of downtown is the trendy South Congress area, Travis Heights, and Barton Hills. All three areas have a lot of nice bungalows and smaller houses for reasonable prices. At the law firm where I work now, a lot of the new associates live in these areas. There are also abundant food options and there is little-to-no traffic to get downtown (assuming your law offices will be located there). North of the river, Clarksville is just west of downtown and has similar houses, but is more expensive. West of campus is the Bryker Woods area, which is also a little on the expensive side. North of campus, Hyde Park has a lot of young professionals and grad students living in it. All of these neighborhoods have great character, with great local restaurants and entertainment options nearby, and are moderately affordable.
In terms of places to stay, Hotel San Jose on South Congress is one of my favorite places to recommend. It's definitely one of the coolest hotels in the city. Aside from that, you really can't go wrong with any of the hotel options downtown. If you're looking to splurge, stay at the Stephen F. Austin or the Driskill, two of the nice, old, local hotels.
In terms of activities, these are some things that I always take visitors to when they visit Austin:
1. Whole Foods. Whole Foods was founded in Austin in 1980 and is headquartered here, and they recently built their flagship store downtown beneath the headquarters (the largest Whole Foods in the world, I believe). Go for lunch--there are about 15 different food stations inside and it is an awesome experience.
2. Mount Bonnell. Touristy, yes, but for a reason. One of the highest points in Austin, this gives you a gorgeous look at Lake Austin and the hills to the west. Make sure you walk around a little bit so you can take a look at the view to the east and see downtown.
3. Barton Springs. Austin in all its glory. A natural spring-fed swimming pool that rests at 68 degrees year round, this place is always packed with Austinites trying to escape the heat (wow, I think I'm beginning to sound like a tourism-book writer). In the heart of the city, you really can't go here and not fall in love with Austin.
4. South Congress. As I mentioned before, this area is really trendy and has a lot of cool local shops and restaurants along it. Has some fun bars too (Hotel San Jose Bar, Doc's Motor Works). If you eat here, go to Guero's (or Vespaio if you want to spend a lot of money). Make sure you stop in and take a look around Allen's Boots.
5. If you're into exersize, hit up the trail around Town Lake. There is a three-mile, four-mile and six-mile option, and the people watching opportunities abound.
I could go on and on, but this should give you enough reading material for now. Let me know if you have any questions about anything else (good restaurants, more stuff to do, etc.) and I'd be happy to help.