My rankings are based purely on where I don’t mind laying over for a few hours since I fly out of a small airport (RNO) and am always connecting. I favor a good lounge or two and the ability to walk distances to kill time.

For true AA hubs:

LAX for walkability and multiple lounges - the T5 Admirals Club is usually uncrowded and the Alaska lounge is great. Flagship Lounge is nice too.

ORD for the same reasons. I love the H/K Admirals Club.

DFW for the Flagship Lounge and the AA employee store - an avgeek's dream.

JFK just for the TWA Hotel, which is an absolute must visit.

For non-hubs:

SFO Terminal 1 might be the most beautiful terminal in the AA system and the AC there is quite nice. As mentioned upthread, the lack of announcements make it so peaceful. SFO has really grown on me over the many years of improvements. Only downsides are that walkability sucks as T1 only connects to international A gates, and somehow doesn’t connect airside to Alaska’s D gates and outstanding lounge. I hope this is resolved soon.

SEA for the Alaska lounge, best in their system. You can also walk/train and explore for days there.

I also enjoy AUS for the decent retail options and live music.

There are countless other airports I really like, but can’t really consider them “AA airports” per-se.