Bars in Omaha

If you want a good tap selection and a good patio, I would head to Krug Park or Jake's in Benson. Downtown Upstream has two great patios, but the beer is better at Krug and Jake's. There are obviously lots of other good beer bars in town (Crescent Moon, etc.), but those are the only ones I can think of (off the top of my head) that will meet both of your criteria.

 

Downtown:
Upstream (as above)
Wilson & Washburn (no patio, but great food and tap selection)
Borgata Brewery/Distillery (patio, decent in-house brewed beers, great guest taps)
Blatt Beer & Table (great food, beer, upper and lower patio)

Midtown:
Beercorner USA [Crescent Moon/Max & Joe's/Huber Haus] (great beer and food, no patio)

Benson:
Krug Park (as above)
Jake's (as above)
Benson Brewery (good food, decent beer, new beer garden)
Infusion Brewing (great beer, snacky-foods, no patio)

West Omaha:
Upstream Legacy (great beer, food, and patio)

 

Yeah, I totally forgot about Borgata's tiny patio And the great patios at Blatt.