You can go off post if they accept Tricare. If that is the case, you MAY be able to be seen with Tricare Prime. However, you typically have to switch to Tricare standard. This involves a small copay. I think ours was around $10 per visit. I preferred this because civilian providers were almost always able to get you in same day. With the military, you have to call at exactly like 7am and it is first come first served for sam eday appointments. Once they are gone, you have to try again tomorrow.
I was at Fort Bragg when my kids were born. We went off post due to Fort Bragg not having a nursery in the hospital. Also, the civilian hospital just seemed a little easier. That was covered under Tricare prime.
I felt it was a headache being seen on post, and I still feel that way. I would prefer being seen in a civilian practice due to the ease of getting an appointment.