The Adirondack Railroad runs heritage railway excursions from Utica's Union Station north into the foothills and forests of the Adirondacks. It is transport, technically, but the point is the ride: old rail stock, slow scenery, seasonal trips, and the pleasure of leaving the city by train rather than by highway.
Most visitors board at the historic station on Main Street, which is worth a look in its own right. Check the schedule carefully, because services are seasonal and themed trains can sell out. The longer trips make this a proper day out from Utica, while shorter runs work well if you simply want a taste of the old Adirondack line.