Mordor. The nighlife would be downright boring (and violent to boot), but at least there's fireworks.
Dale/Laketown would be an interesting place to have an inn-type thread. It's got three major races in the immediate area, and largely undeveloped after its mention in the Hobbit. I think a post-Hobbit pre-WoTR Dale would be an ideal setting. Plenty of rebuilding, trading, and other sub-plots to last a lifetime.
I think anything during the reing of Aragorn/Elessar would work fine. Most of the major political players are still alive, and Tolkien has a fairly good outline of events for the era.