There are three airports close to Hamilton County:
Cincinnati/Northern Kentucky International Airport (CVG)  is on the Kentucky side of the Ohio River, so you'll have to cross the bridge to get to Cincinnati itself. Delta has its second largest hub here.
Dayton International Airport (DAY)  is about 50 miles to the north.
Cincinnati is served by Interstates 71 (from Columbus and Louisville), 74 (from Indianapolis), 75 (from Dayton and Lexington), 471 (a spur of I-71- to the south), and 275 (the circle beltway). US 50 also serves the area as an expressway to the eastern neighborhoods (Columbia Parkway) and western neighborhoods via the Sixth Street Expressway, which links River Road and the Waldvogel Memorial Viaduct to Downtown.
One of the most beautiful panoramic views in the country occurs when driving northbound on Interstate 71/75 (the interstate routes share the same highway in part of Northern Kentucky) travelling into downtown Cincinnati, just before the Brent Spence Bridge.
Amtrak, offers passenger train service from key U.S. cities. All trains arrive and depart from Union Terminal/Cincinnati Museum Center. This is several miles from Cincinnati, and since most of the trains arrive before dawn, before public transportation is available, it may be wise to call a taxi to finish the rest of your journey. (See Taxis.)
Greyhound  offers passenger bus service from many U.S. cities. Buses arrive and depart from Greyhound's station in downtown Cincinnati.