You can probably open the museum without setting up a separate 501(c)(3) charitable organization. Veterans’ organizations that qualify for exemption under section 501(c)(19) of the Tax Code are heavily favored by Congress and have unique privileges, so long as their membership is composed almost entirely of veterans and their family members.  75% of the members must be past or present members of the U.S. Armed Forces or students in college ROTC programs or the military service academies, and 97.5% of total members must be such service members or their spouses, widows, widowers, ancestors or lineal descendants. 

If these criteria are met, the organization may provide social activities for its members (normally provided by 501(c)(7) social clubs), assist disabled and needy veterans (a (c)(3) charitable activity), provide insurance benefits for members and their dependents (activities permitted in 501(c)(8), (9), and (10), promote social welfare in the community (permitted in section 501(c)(4)), and conduct programs of religious, charitable, scientific and educational purposes (generally permitted in 501(c)(3)).  The best part of all this is that contributions to a (c)(19) veterans’ organization are generally deductible by the donors as charitable contributions. 

Therefore, if your museum would qualify under section 501(c)(3), you could probably do it within your (c)(19) veterans’ organization without having to set up a new organization to obtain separate exemption.  A gift for your museum would ordinarily be deductible.  If you were a (c)(4) social welfare organization or a (c)(7) social club, you would need to set up a separate (c)(3) organization if you wanted your donors to be able to claim the charitable contribution deduction.  Your organization, too, could set up a separate 501(c)(3).   But a (c)(19) veterans’ organization can do a whole lot more within its existing exemption.  (See IRS Publication 3386, Tax Guide for Veterans’ Organization.)