Most certainly does! VFW for sure, but I'd check the Legion base to be sure.
I tried the VFW for a few years back in the late 70's. Too many Carter supporters. I'll try the legion.
Probably not eligible for VFW, unless you served in Thailand in support of ops. I don't know about at Anderson, I would think that would do it too, if you served there during the Vietnam war. However if you never served overseas, then you are not eligible for VFW membership, it is after all the Veterans of Foreign Wars. You are definitely eligible for Legion membership. Your period of service brackets mine, and I am eligible and was a member, but I let it lapse when I moved. Basically if you are eligible for the national defense service medal, you are eligible for Legion membership.
My Dad belonged to both, plus the DAV (a branch of which is visible from Mom's house). Check here for VFW eligibility (PDF file!) and here for Legion eligibility (also PDF, it's the application form)