The Cincinnati Art Museum sits in Eden Park, a hilly green space east of downtown with views down to the Ohio River. The collection of over 67,000 works ranges from ancient Egyptian art to contemporary American painting, but the highlights are the medieval and Renaissance European holdings, the exceptional American furniture and silver, and a strong section on ancient Near Eastern art.
The museum building is worth looking at as well — a neoclassical structure that has been expanded several times, most recently with a contemporary wing that handles the transition from old to new without embarrassment. The sculpture terrace behind the building gives a view over the park. Free admission (for the permanent collection) makes this an easy choice for an afternoon.