This (almost) exact scenario played out in Marsh v. Alabama (https://en.wikipedia.org/wiki/Marsh_v._Alabama). If the town is, for all intents and purposes, acting like a traditional town, and with the public having access to it, first amendment rights hold.

Also, worth reading up on Manhattan Community Access Corp. v. Halleck (https://en.wikipedia.org/wiki/Manhattan_Community_Access_Cor...)