The Zane's Landing Trail is a nice and level ride from the dock of the sternwheeler Lorena on the eastern side of the Muskingum River in downtown Zanesville north between the river and the Ohio Central railroad tracks to Riverview Drive near Riverside Park. Parking at the southern end is paved and plentiful and is found near the trailhead at 39-56.634N and 082-00.602W. There is also parking in Riverside Park just a bit south of the northern terminus at 39-58.565N and 081-59.040W. The entire 2.9-mile trail is paved and relatively smooth enough for road bikes. I consider this only a "fair" trail due to the short length, lack of shade, and mediocre riverside scenery.
However, I would encourage riders to park near the Lorena mooring and, after riding the 5.8-mile round trip, leave your car where it's at, and continue south one more block to Zanesville's historic Y-Bridge that was originally built in 1902 over the confluence of the Muskingum and Rocky Fork Rivers. The center of the bridge can be found at 39-56.420N and 082-00.862W. The view looking south along the Muskingum River is quite scenic. Looking north, one can see beyond a railroad bridge to the Lorena in her mooring.
If you would like to see more of the Muskingum River scenery, drive north along OH-666 into Dresden and ride the Muskingum Recreational Trail. Parking is in a private lot (that the owner has approved) near the northern trailhead at 40-06.552N and 082-00.707W. From there you can ride 4.0 miles south and southeast along the western side of the river to the southern terminus at 40-04.129N and 081-58.623W for an 8-mile round trip. This trail is 100% shaded the entire distance as it meanders through the woods. There is parking at the southern terminus although it is really in the middle of nowhere. Parking at the northern end is in the jurisdiction of Dresden Police and appears to be the better choice. Because this trail runs entirely through the woods there are numerous surface irregularities that are fun for mountain bikers but that might annoy road bikers.