SovangW, it really depends where you're located at, what your home/personal situation is, what your long-term goals are. To be honest, every culinary school has a Veteran's representative that deals with any post-military affiliate whether you came in from the German Army or U.S Coast Guard, etc so finding a school that will help you out with activating your GI bill or finding a veteran to tell you about what going to the school is like won't be a problem.
Okay, so i'm an Army Veteran, culinary school grad, who currently works the line at a fine-dining restaurant and who is going back to school for business this fall. I also used my GI Bill to go to culinary school and what I can tell you is that culinary school does give you a broader understanding of how to produce good food and how to sell good food. I'm not selling you the idea, it's just that I was in the same boat on my way out of the military and culinary school ended up helping a lot.
I would suggest atleast going to culinary school because they give you the basics on how to supervise a kitchen, who you need, and why, how the front-of- house and back-of- house operates together to complete a successful dining service, how to cost out food so you know how much to charge customers so you can pay yourself and pay your overhead costs, laws, working with the Health Department, industry trends, how to save money, etc. I even had to write out a complete business proposal for a restaurant that I "planned on opening"; the sucker was a huge binders worth but i'll have it as a hardcopy example for the day I do finally open up my own place. Also, I walked out of school with a college degree, nutrition, ServSafe, and Alcohol Safety certification, and a lifelong network.
Or you can always find a place that is similar to a place that you want to open up and then work your way from the bottom up and hope that your boss is cool enough to show you the business side to things. In real life, the restaurant is separated into a venn diagram; front-of-house on the left, back-of-house on the right, business sits smugly in the middle.
Feel free to PM me or whatever if you have any other questions. Good luck and thank you for your service!