Veterans allowed but not sure what you mean any-time. Time time or a actual date. If you mean time it's free for all but buying a pass gets you in at a earlier time. You will have to call and ask if veterans are exceptions to also get anytime access without paying for a pass.
You can find all the info regarding passes/entry and contact info here https://nmaahc.si.edu
Yes Veterans can visit without a pass. You'll just need to show your military, work id or badge to verify your status. You're also allowed to bring 1 guest being a Veteran. 1-844-750-3012
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