Awesome. Enjoyable diving is quite subjective.
I also learned to dive at Ft. Lewis (what JBLM was known as back in the day) in 2002. I signed up for lessons at The Northwest Adventure Center. I offer what I hope will be good insights for you. The first three will be where I have been assigned, and then I'll follow with some places that I know offer access to diving. I'm not fully updated on what some of the Army installations have changed their names to. So I'll just use their names when I was on active duty. I did 20 years and retired from the Army in 2019 (20 years was more than my fill of fun and BS).
Besides Ft. Lewis and the Puget Sound...
1. Schofield Barracks (and/or Ft. Shafter). All the Hawaiian islands offer scuba in one way or another. Oahu offers the best IMO in both shore diving galore and boat diving. Maui and the Big Island offer great diving also. You can probably get access to Lanai via some dive shops on Maui. You'll have to do your homework for diving off Molokai. My dive shop on Oahu, Island Divers Hawaii (they changed ownership; I don't know what the new name is), sometimes offered overnight charters to dive Molokai. You can hit up MWR or Leisure Travel Services for lodging options on the Big Island for less money than a typical tourist. Oahu is a great place to get technical dive training and certification because the conditions are ideal for training. I did my gas blending and tech certs while there. Hawaii tops it all when it comes to Army installations with access to scuba diving.
2. South Korea. There is diving off Jeju Island to the south of the Korean peninsula. Not the greatest diving but something different. Getting stationed at Camp Humphreys or Camp Walker will get you access to Korea diving. I dived Jeju Island in month of May; water temps were mid-60s. But the big ticket is access to diving areas such as Philippines, Thailand, Indonesia, Japan, many of the Pacific islands, etc.
3. Military District of Washington/Ft. Myer/Ft. Belvoir/Ft. McNair etc. Maybe some installations like Ft. Lee or Ft. A.P. Hill. While not the most coveted dive destination in the world, you will have access to Atlantic Ocean diving options and quarries, lakes, and rivers on the East Coast. I found a non-profit based in Maryland called Institute of Maritime History (IMH) who I volunteered with. Their specialty was archaeological diving to survey wrecks in the Potomac and Chesapeake Bay. If you want to level up on your diving skills and are confident then give them a try. You will encounter blackout conditions in which you can't see past your mask, mud, strange submerged things, entanglement hazards, bull sharks, flesh eating bacteria called Vibro vulnificus. It's better to dive solo than with a buddy because you'll just lose your buddy in the muck and darkness. You will all enter as a group, but after descent you'll all get separated. Quite challenging conditions but all your dives are free of charge with IMH!
Other places that will give you decent access to diving:
1. The Presidio of Monterey, California. Access to great diving at Monterey Bay and conditions similiar to Puget Sound.
2. Fort Stewart, Georgia. Easily within reach of Gray's Reef National Marine Sanctuary off of Savannah, Georgia.
3. Ft. Rucker, Alabama. Striking distance to all the diving in Florida panhandle and south Florida.
4. Ft. Bragg, North Carolina. The best draw is Morehead City, North Carolina to dive the Graveyard of the Atlantic.