Cincinnati lies along the north bank of the Ohio River, between where the Great Miami and Little Miami Rivers flow into the Ohio. Dayton is about 55 miles north of Cincinnati on the Great Miami River, and Columbus is 110 miles northeast of Cincinnati, where the Olentangy flows into the Scioto River, a relict of the Teays. The Miami Rivers are so named because prior to American colonization, the rivers were the eastern boundary of the lands of the Miami (1). To the east and south (in Kentucky) were the traditional lands of the Shawnee around Chillicothe and the lower Scioto.
The Carew Tower (441 Vine St) is Cincinnati's tallest building, and apparently it's panoramic observation deck is open daily.
Southeastern Ohio includes some of the most significant ancient archaeological sites of the midwest and Ohio River Valley, Serpent Mound, the largest effigy earthwork in the world, and Fort Ancient, a key site of the upper Ohio Valley moundbuilders. Near Serpent Mound is the Davis Memorial Nature Preserve. In central Ohio, there are several Hopewell moundbuilders sites (Great Circle, Octagon, Wright, and Seip Mound), as well as Flint Ridge and some Adena sites (1, 2). The Hopewell Culture National Historical Park is near Chillicothe.
The Ohio River Trail is a bike path running trhough Cincinnati that will connect to the Little Miami Scenic River Trail and eventually to the planned Ohio to Erie Trail, on which one could cycle on 453 miles all the way from downtown Cincinnati to Lake Erie at Cleveland. ORW also hosts the Ohio River Swim and Paddlefest.
The Bicycle Museum of America is way out in New Bremen, Ohio. I thought it had something to do with the Wright brothers, but they were from Dayton, where the National Museum of the United States Air Force, the Dayton Aviation Heritage National Resort Park, Paul Laurence Dunbar House, and SunWatch Indian Village are. The area around New Bremen has some remaining sections of the Miami and Erie Canal. Miamisburg Mound, the largest conical burial mound in Ohio, is south of Dayton, as is Fort Hill.
Morgan's Raid is the most significant engagements of the Civil War fought in Indiana and Ohio. The only remaining fortification remaining from the Civil War emergency defense of Cincinnati is Battery Hooper at the James A. Ramage Civil War Museum, which was filled in with dirt, in Fort Wright, Kentucky. The defense of Cincinnati was the occasion of the first bridge across the Ohio River there, a military pontoon bridge.
Cincinnati was one of the most significant links in the Underground Railroad and the western abolitionist movement. The National Underground Railroad Freedom Center was established in 2004. Other Cincinnati museums include the Cincinnati Art Museum, Cincinnati Fire Museum (the nation's first municipal fire department was established in Cincy in 1853), the Cincinnati Museum Center of History and Natural History and Science, the American Sign Museum, and the Harriet Beecher Stowe house. Southeastern Ohio also includes the Ulysses S. Grant birthplace in New Richmond and boyhood home in Georgetown, the National Afro-American Museum in Wilberforce.
Here's the Best of Cincinnati 2009, including Urban Life and the hills.
There are plenty of state parks in Ohio. In the area around Cincinnati, the most significant state parks and natural areas may be Clifton Gorge State Nature Preserve, Caesar Creek Gorge State Nature Preserve, Little Miami State and National Scenic River, Little Miami State Park, Caesar Creek State Park, and John Bryan State Park, as well as Brush Creek State Forest and Stonelick State Park. Ohio's only national park is in the north between Akron and Cleveland.
It'd be something of a drive past Cincinnati, but we could always get some Kentucky flags and drive to Portsmouth, Ohio, to protest the theft of the Indian Head Rock by those buckeyes up there.