I have not tried this with a small town government, but I have had some relevant experience running an independent Discourse-based community site in an institutional setting.
My main lesson is that the technical side is probably the easier part. Discourse itself can work very well for structured discussion, announcements, categories, moderation, events, and long-term searchable conversations. The harder questions are institutional ones: who is responsible for moderation, what counts as an official statement, how public-facing the site is, what authentication method is appropriate, how data/security concerns are handled, and whether users might wrongly assume the site is officially endorsed if it is only semi-official.
For a town government, I think the hosted Discourse option would make a lot of sense if they want this to be an official public communications channel. It reduces the burden on a volunteer or one technically minded resident, and it gives the town a clearer support route if something breaks. A self-hosted setup might be cheaper, but then the town would need to be comfortable with who is maintaining it, how updates/backups/security are handled, and what happens if that person is unavailable.
I would also be careful to define the site’s role from the start. For example, is it an official noticeboard? A public feedback forum? A resident discussion space? A visitor information board? Or some mixture of those? Those are quite different use cases, and they probably need different moderation rules.
In my own experience, it is worth being very explicit early on about independence, endorsement, login/account handling, moderation responsibilities, and escalation routes. Discourse can provide the platform, but the institution still needs a governance model around it.
For a small town, I could imagine it working well if it starts with a narrow scope: announcements, events, planning updates, public Q&A, and clearly moderated resident discussion. I would be more cautious about launching it as an open-ended “anything goes” town forum without clear staff ownership and moderation boundaries.