No (unless you are a military dependent) This is for a couple of reasons.
1. security. A civilian is typically not permitted on US bases without a dependent id card or an escort by either a dependent, civilian contract worker, or military member. That is for obvious reasons.
2. There is something called the status of forces agreement. Some of these agreements include ones that are financial. Meaning that it would probably be cheaper for you to eat on base than on the civilian economy.