Honestly you can't go wrong with any of your choices.
My wife is stationed in Ft. Walton. For base courses you have the course on Hurlburt (fun place and in pretty good shape), two courses on Eglin (one of the courses is in the discussion for best DOD courses), and then Tyndall isn't too far away. For off base golf you don't have anything that is top 100 quality but it's affordable and pretty good (lots of places offer military discounts).
Tampa is the area I know the least about but a resort that may become Bandon Dunes of FL (
http://www.streamsongresort.com/
) is going to be opening pretty close by at the end of the year and I wouldn't be surprised if both of the courses there become the top public courses in FL.
We have a place in Pinehurst. There are people that live in Pinehurst and drive to Bragg (about 45 min to the main gate from Pinehurst). As far as the military courses the two courses at Bragg are probably the worst military course options of the four places you listed, but certainly not the worst military courses there are. That being said there is a lot of other public golf options in the area that are really good. I'd recommend the bit about living in Pinehurst. Most of the residents are a bit older but it has a good community feel. If you have kids it's safe, there are pools, there is the lake and the golf is great. Pinehurst often gets billed as being expensive golf but if you buy a house and join the Pinehurst CC you can play #1-#6 and your membership fees are reasonable for the quality of the golf you get (the fee per month is less than the walk up rate on #2).
I started my career in Co Springs and can't wait to get back. I've played 100's of rounds on the two courses at the AF academy. The Blue course is my favorite DOD course. The course on Fort Carson is pretty good and Peterson is alright. People have knocked the fact that there is a golf season. I can tell you I played in every month of the year (occasionally the turf was frozen but I was still playing) while we lived there. The mountain states are definitely under rated golf states.