Rainey Street has undergone some development in recent years. The funky little places are becoming high rises. Bangers has Artisinal Sausages and 100 taps of beer. Craft Pride may not be there anymore, hard to tell.
The area between 4th and 6th east of I-35 has some good stops. Brew and Brew is coffee and and a multitap. There are several Breweries and restaurants sprinkled in there. I see there is an Easy Tiger location nos, and the old one on 6th street doesn't come up. 6th street west of I-35 is the college crowd party district that gets hosed down in the mornings.
Rainey Street has gone through a lot of changes. Many of the bars are gone, including Craft Pride. Bangers is still there.
Easy Tiger left 6th and moved on the other side of I-35. There's a lot of breweries and good restaurants over on that side of town.
--
There are a lot of new breweries open in Austin since I moved out of the state. I agree with recommendations for Live Oak, Pinthouse and ABGB. I'd also try to hit Austin Beerworks if you're on the north side at all. Live Oak is right by the airport. Pinthouse has three locations around Austin. There are a cluster of breweries around Austin Beerworks. That area south of downtown has a lot of good food and brewery options but a little more spread out. It's not hard to burn a day hitting breweries in that northwest corner, or south of downtown, or east of downtown.
Austin doesn't have a lot of beer bars but there are a few if you're trying to taste more beers but move less. Bangers is a solid choice. Austing Draft House brews their own beer but also has a good list. They are in the northwest down the street from a Pinthouse location. Easy Tiger will have a small but good list. Oddly enough some of the Whole Foods grocery stores will have a decent list at their growler stations. Alamo Drafthouse Cinema are movie theaters with good beer bars. You can drink at the bar without seeing a movie. Barber Shop in Dripping Springs if you get thirsty heading that way. Whip In south of downtown usually has some good options. I would look online at the list of any of these places before driving over. Sometimes the lists aren't great or not what you like to drink.
Of course, if you really want to derail that trip west about halfway out you can drop down to Real Ale in Blanco and/or go up to Johnson City where there are a few breweries, some good bars and some wineries. Shortly before Dripping Springs you can hit Jester King. There are a couple other breweries over there and I believe there is/was a meadery. I believe there's also a winery right there.
One thing I will say is to think a lot about traffic and time to move places. The freeways will be at a crawl during rush hour during the week. If you're there during a UT football game you'll want to avoid I-35 that entire day. Everywhere near the university and downtown will likely be packed all day and remain packed all night if they win. That stretch of 290 exiting Austin to the west is always a mess and absolutely a mess on weekends. The intersection at 290 and 71 is usually packed on the weekend and it's confusing. Look at the intersection on the map to make sure you head out the right way. It's a long detour if you end up on 71 instead of 290. It's a nice drive once you get past that intersection.
On the subject of BBQ--unless you care a lot about BBQ you'll be happy eating brisket at any of the places named above. Franklin's is the tourist trap and the line will be long. If you care about saying you went to Franklin's then you should go. If not, I would look elsewhere. Terry Black's, La BBQ, Micklethwait are all well regarded options. If you go to Franklin's and balk at the line, Micklethwait is right down the street. There are several others right in that area. If you have a few people with you or an especially large appetite, you can pre-order Franklin's and skip the line. You have to order I believe at least five pounds of meat.