Veterans and military service members who die in the line of duty all have the right to request to be buried in Arlington National Cemetery, from what I understand, but there is no custom, mandatory or otherwise, that I'm aware of that says veterans HAVE to be buried in a particular location. Considering that most people prefer to be buried near where their families live, I'd say most veterans would NOT want to be buried in a particular location, whether it's a cemetery specifically built for veterans or not.
My grandfather was a WWII and Korean veteran who died as a retired colonel, full-bird; as such, had he wanted to, he could have likely been buried in Arlington, but he chose to be buried near the area he was living in. Fort Lee DID send a full funeral detail to his funeral, but that's the extent of the involvement the military generally has with a veteran's or servicemember's funeral; the actual details, such as location, whether they want to be cremated or not, etc and so forth, are dictated by the soldier in question via a living will or other legal documentation. Granted, not all soldiers have those, but in those cases I believe they defer to the next of kin to determine burial rites. It is in no way dictated by the military or the government.