You guys are the best. We are mid-40s but play like we're in our mid 20s. Right now I have reservations at the JW Marriott & the Hilton downtown.
Here's my long take on some of the entertainment/bar districts in the downtown core. We have so many areas, I'm know I'm missing a ton of recommendations. I didn't even mention South Congress here because it's not in the center of downtown but it's worth checking out. All of the stuff below will be walking/pedicab distance from your hotel except for E.6th. I've heard that the underpass under I-35 between the east and west can be sketchy late at night, you may want to take an Uber across. Don't let that scare you though, in general Austin is extremely safe.
Dirty 6th:This is the famous (infamous?) part of 6th with tons of bars, but it's mostly a younger (college to upper 20's) crowd. This is the part between Brazos and I-35. You might want to stroll down it just to see it though and there are some good spots. Generally several bars here will have live music with low or no cover charges. My favorites are BD Riley's (Irish pub), Driskill hotel (oldest hotel in town, highly recommend a walk through), Midnight Cowboy (speakeasy cocktail bar, make reservations), Maggie Mae or Blind Pig (rooftop people watching), Firehouse Lounge (cocktail speakeasy, nifty entrance behind a bookcase), Easy Tiger (German beergarden-ish), Casino El Camino (dive bar with great burgers), Pete's piano bar is popular with tourists but I'm not a huge fan, haven't been in many years though.
West 6th: 6th St between Lavaca St to West Ave. Some OK bars here but also a bit of a "bro" area these days. Mid 20's to mid 30's crowd. Check out Dogwood, Key Bar, Wahoo's Fish Tacos, Hut's burgers, Frank & Angie's Pizza, Little Woodrows.
East 6th/East side: Hipsters. Hipsters everywhere. Some cool bars though, many of which I haven't been to. Basically 6th east of I-35 from Medina to Chicon-ish, but there are bars off 7th and 5th over here too. Note that 6th St. is technically E.6th when you get East of Congress Ave, but if someone refers you to E.6th as a district, they likely mean east of I-35. I like Yellow Jacket Social Club (good for casual brunch). I haven't been to many others in this area. It's also home to Qui, home of fine dining by famous chef Paul Qui. Via 313 is Detroit style pizza and they have a truck at Violet Crown Social Club (bar). It is fantastic pizza but a little spendy. Get the Detroiter (pepperoni). The have a second truck on Rainey St at Craft Pride (Texas craft beer bar).
Red River: Mostly a live music stretch of downtown containing small concert venues. A pretty diverse crowd due to the music draws, it really depends on the bands that are playing. This runs along Red River from 6th St to Mulberry St. There are some cool venues here but some are more for concert viewing than a random pop-in (Stubb's and Mohawk in particular). Cheer up Charlie's is a good pop-in sort of place though, as are some of the spots around 7th St.
Rainey St. - Along Rainey St between Driskill and River St. A street that contained a bunch of old houses until someone noticed that this area wasn't zoned to be only housing. Someone bought an old home and converted it to a bar (Lustre Pearl, no longer there due to condo construction), and the rest is history. Tons of people did the same and now the street is full of converted homes that are bars. It's one of my favorite spots downtown because the bars are pretty casual, although in recent years this area has seen an influx of some of the W.6th crowd and lost some of the casual vibe it once had but you won't be out of place here at all. The upcoming condos will likely exacerbate this though. You can walk down this street and pop in anywhere. My favorites are Bar 96, Banger's (in-house made sausages, 100+ beers on draft) and Craft Pride (all Texas craft beer on draft, excellent Via 313 pizza truck in back). Blackheart usually has live music. Container Bar isn't my favorite, but it's uniquely made out of shipping containers.
Warehouse District: A few blocks around 3rd-5th St, between Congress and Guadalupe. There is a high concentration of bars between Lavaca and Colorado, on 5th St. There are few gay bars in this area and quite a few restaurants. Frank is a popular hot dog joint. Truluck's is upscale seafood. I like Lavaca St. Bar and Gingerman (~100 beers on draft). This also draws a diverse crowd. It used to be that older folks came here after "graduating" from dirty and W.6th but not so much anymore, now it's just a mix of everyone it seems given it's proximity to the other downtown spots.
2nd St - 2nd st between Congress and San Antonio. This is newer, semi upscale district with newer places vs. the other parts of downtown. It's more for dining and shopping but there are a couple of bars. We love Second Bar & Kitchen Trace at the W hotel is an upscale bar. La Condesa is a good Mexican restaurant. This area tends to be an older crowd with more money to spend.
A few others that I wasn't sure where to put them - Elephant Room (Jazz club), Cedar Door (casual bar, longtime Austin local favorite), Swift's Attic (upscale Tapas), Perry's (my favorite steakhouse in town), Sullivan's (good steakhouse)