I suspect that some of the nicest airports served by UA are some of the smaller ones since they are easier in terms of lay-out, short security lines, friendly feel, etc. But I don't get to those too often, so among the larger ones...

I may well be biased because it's my home airport (and my more general bias in favor of northern California), but I like SFO a lot. That being said, it can get fogged in with resulting delays, and security lines can be long for non-elite flyers (and sometimes for elite ones). Still, I like the lay-out, food choices, usually friendly personnel there, spaciousness, views from some spots, etc. I tend to think that it's the nicest major airport in the USA.

I love Singapore's airport for different reasons: It's almost like a mini-city, yet quite efficient. Hong Kong too--not as interesting as Singapore, but beautiful views from some spots and quite easy to navigate even though it's such a major facility.

I've come to intensely dislike FRA as a complex, unwieldy center that can be tough to figure out even having been there before. Security and otherwise transferring between flights can take a long time, with posted information often incomplete or missing. Someone somehow seems to have left out the very admirable German efficiency in designing and running this airport.

Domestically, not a big fan of LAX, JFK, LGA, ORD and especially IAD, for various reasons.