Last time I went home to Springfield (IL) I heard about an interesting controversy brewing. The city passed a ban on smoking in public places that was then mirrored by the county. There exists a man-made lake (called Lake Springfield) that is lined by private boat clubs. Most of the clubs are located outside of the city borders and used their clout in the county to get "private clubs" exempted from that ban.
Apparently though, although the land is outside the city, all the land under and around the lake is owned by the city. The clubs exist there by grace of long-term leases on the lands from the city. The city mayor has declared that the city will use their rights as landlords to send city cops out there and enforce the city ban.
This is an interesting conundrum I think. On the one hand the city is a landowner and has the right as such to enforce the rules it lays down on the land. But a private landowner would have to go through the county sheriff to get such rules enforced rather than send in his own police force, and I'd think the rule would have to be in the lease. So on the other hand, you have a government sending its police outside its borders (for reasons other than hot pursuit) to enforce its own laws.