Good brews in Omaha, NE?

Not a problem. For breweries, definitely hit Infusion and Nebraska Brewing Co. (I sadly haven't kept up with the 'recent wave' insofar as quality, being Borgata, Benson Brewing Co., Farnam House, and a bunch of others that don't jump to mind). For bars, hit Benson (Beercade/Jake's/Krug Park), Crescent Moon, and maybe the Brix locations (as of Saturday the Village Point location had Surly/De Proef Long of Tooth, NE Brewing Co./New Holland Attack of the 50-Foot Brown, Stone XOCOVEZA, and others on). For bottle shops, hit Beertopia (right next to Crescent Moon), Stony Brook Hy-Vee, Cubby's (for older releases that sell out at other shops), Mall of the Bluffs Hy-Vee (for Iowa-distro beers: Evil Twin, Mikkeller, Crooked Stave, Jolly Pumpkin, Prairie Artisanal Ales, occasional Drie Fonteinen/Tilquin, Bell's, Left Hand, and a whole lot of others), and for specific beers ask (here or in the other thread).

For beers to try or bring back, and also looking at recent releases:

NE only:
-Most Boulevard. 6-packs tend to be generally good for what they are, but look to 4-packs and their Smokestack series (bombers) for great stuff. Things like Love Child No. 4 (sour), Bourbon Barrel Quad (just released again, may not have hit the area), Two Jokers (sour-ish witbier), Saison Brett, and about anything else in the Smokestack series are all solid. Their Saison collaboration with Ommegang just hit, but I haven't had it yet. Be wary of any Reboot (White IPA) that you see around as it's several months old.
-CIB is generally pretty garbage, don't waste your money on it.
-As is Storz, a revival of a 'historical' brand, and while I haven't had any of their beer yet everything I've heard has been extremely negative.
-Funkwerks does some good saisons and sours - not everything they do is up my alley or has been a hit with me, but I know that people kill for it and they haven't had a 'bad' release that I've had yet.
-For Infusion, absolutely try their Vanilla Bean Blonde. Initially brewed as a one-off, it's now (as best I know) their biggest seller. Great 'light' (on ABV) beer with a solid flavor profile. IMO their best offering. Their one-off releases have been hit-or-miss with me, but their main lineup has been good and I'd generally consider them the best brewer in the state.
-New Belgium is a big one; their year-round profile (sixers) is generally pretty weak; Fat Tire has a decent reputation, but IMO it's just a decent lager. Their most recent seasonal, Tour de Fall, is great in my opinion and absolutely worth trying - it really surprised me when I first had it. On the other hand, their limited bomber series (Lips of Faith) is generally pretty good. New Belgium is a great example of a brewer that isn't afraid to take chances and experiment; the releases can be hit-or-miss and somewhat divisive (Coconut Curry Hefeweizen jumps to mind), but there are some mainstays that are phenomenal - notably La Folie (sour, won't be found right now) and La Terroir (sour, just hit the market, probably still around and there's a bunch at the Village Point Brix).
-Odell is another big one; again, decent but forgettable year-round releases (6-packs), but their 4-packs tend to be really good (especially Myrcenary and Double Pils IMO, but check freshness) and bombers are hit or miss.
-Peace Tree, out of Iowa, is a brewer that I haven't gotten a handle on; releases really hit-or-miss, and I can't think of anything I've had from them that I've really loved (No-Coast IPA was probably the closest, but that's gone/old at this point).

As far as shared distribution, things can tend to stick around here (or be fresh) moreso than bigger cities. There are a number of places that stock good quantities of craft that people don't check immediately, such as Whole Foods, the Brix locations, Cubby's, various Hy-Vees, etc. Mirror Mirror, Not the Stoic, and Black Butte XXVI are still around, for instance, as is Stone 18. The best advice I can give in that regard is to just ask regarding specific beers. I'll lastly mention that Stony Brook and Mall of the Bluffs Hy-Vees both have good single selections, while Beertopia will generally break up single bottles for you if they don't have any available of a specific beer.

 

That's a good rundown. I just wanted to add that if you like Belgian styles, definitely check out Farnam House. It's on the same block as Crescent Moon/Beertopia and they're brewing some really great stuff, and their food is great as well. Also, the Upstream, which has two locations, has been doing pretty consistently solid beers lately, they just released a rye porter that I think is fantastic (food is subpar, though). Infusion and Nebraska are good, as mentioned. You can skip Borgata and Lucky Bucket and not feel bad about it. Benson Brewery is fine, but forgettable. Ristaccia gave a comprehensive list of bottle shops, but if you hit Beertopia and the Mall of the Bluffs Hy Vee in Council Bluffs, you'll pretty well cover whats available in the area.