Where are the current US Army Airborne units located?

Italy
173rd Brigade

Germany
4-319 Artillery BN
1-10 SFG BN

Alaska JBER
4-25 Brigade

Okinawa
1-1 SFG BN

Korea
39th SF Detachment

SF Groups:
Bragg, Carson, JBLM, Eglin, Campbell

75th Ranger Regiment:
Benning, JBER, Hunter AAF

160th SOAR:
Campbell, Hunter, JBER

Ranger Training Brigade:
Benning, Dahlonega, Eglin

Bragg has the most:
82d Division, 3rd SFG, Psyops, Civil Affairs, SWC, 528 Sustainment BDE, 1st SF Command, USASOC, USASOAC, the Parachute Test group, Delta, JSOC

There are about 10-20 detachments around the world that are part of the 112 Signal Detachment but they’re all signal and not applicable to you.

It's easier to answer where Airborne units are NOT located. All of this is off the top of my head and to the best of my knowledge, so feel free to correct me: Fort Hood, Fort Bliss, Joint Base San Antonio, Fort Gordon, Fort Irwin, Fort Stewart (minus Hunter Army Airfield), Fort AP Hill, MDW, Fort Drum, Fort Wainwright, Fort Riley, Fort Leavenworth, Schofield Barracks, Fort Hunter-Liggett, Joint Base McGuire-Dix, Fort Sill, Fort Huachucha, Fort Jackson. Outside of the US, there are Airborne units of various types sporadically located in Germany, Italy, and Korea.