I agree that Rice would offer a great deal of what appeals to you about U Chicago–though the architectural vibe is more Mediterranean than Gothic, and the social vibe is rather more relaxed and laid back than is Chicago’s. Houston is also an easily accessible airline hub, with two major airports.
Wash U offers a similar–if slightly more fratty–feel, and St. Louis is obviously closer to Ohio than is Houston.
Among LACs, Ohio’s own Kenyon College has a good reputation and boasts some of the oldest collegiate gothic architecture in the nation, but it is a good bit preppier than Chicago or Rice. Sewanee, located in a truly rural region of Tennessee, features a stunningly beautiful Gothic campus and some interesting traditions, but its preppy culture and Southern High Church Anglican tenor might not be to your liking.
The LAC most often likened to U Chicago is Swarthmore, less for the campus look than for the noted academic intensity and intellectual focus. The famous Chicago quip is that the school is “Where fun goes to die.” The corresponding Swarthmore quip is “Anywhere else it would have been an A.”