How to access military records.

My father passed several years back but I've been curious about his life lately. I attempted a request through the government but I was not listed as next of kin. He served in the Army, deployed to Korea during the late 60s. He never saw combat but I'd still be interested to see his records. As it is, he left me nothing but questions.

As I saw in another post FOIA requests are unlikely to be filled anytime soon. Any advice is welcome.