This is a good example of what a court might draw and why Democrats (mainly the Legislative Black Caucus) should proceed with the referendum and maneuver for a court map.
OH-1: Steve Chabot (Blue)
56% Obama, 42% McCain
I tried to maximize the black population and got 28%, which is close to the 30% district the Legislative Black Caucus wants. It's a swing district, but it requires a lot of work for any Republican, Chabot included. I consider it a swing district, though, because low turnout in the off year would be harmful to a Democrat.
OH-2: Jean Schmidt/Steve Austria (Green)
59% McCain, 38% Obama
The disliked Schmidt would probably still have trouble in waves.
OH-3: Mike Turner, Steve Austria (Purple)
51% Obama, 47% McCain
I wanted to create Dayton centered district, without splitting counties too much and this looked like the best option. It's a swing district that either party could win.
OH-4: Jim Jordan (Cadet Blue)
63% McCain, 34% Obama
OH-5: OPEN (Medium Spring Green)
51% Obama, 46% McCain
This was a leftovers district that I formed after trying very hard to make a compact district with some leftover counties.
OH-6: Steve Stivers (Teal)
53% McCain, 44% Obama
Stivers doesn't have his bank buddies, but it's still a safe seat.
OH-7: Patrick Tiberi, Bob Gibbs (Grey)
56% McCain, 41% Obama
OH-8: John Boehner (Turquoise)
64% McCain, 34% Obama
OH-9: Marcy Kaptur/Bob Latta (Royal Blue)
58% Obama, 40% McCain
OH-10: Jim Renacci (Pink)
50% Obama, 48% McCain
OH-11: Marcia Fudge (Bright Green)
82% Obama, 16% McCain
49.9% Black, which should be enough to past the VRA test. Since it's overwhelmingly Democratic, the primary electorate is what counts and it is no doubt sufficiently black.
OH-12: OPEN (Cornflower Blue)
68% Obama, 30% McCain
This Columbus-area seat is almost exactly the same as the one on the GOP map.
OH-13: Betty Sutton (Salmon)
55% Obama, 43% McCain
Slightly better than her current seat.
OH-14: Steve LaTourette (Olive)
51% Obama, 47% McCain
Making things more compact gives LaTourette a more Democratic seat.
OH-15: Tim Ryan (Orange)
58% Obama, 39% McCain
Canton is added to this district, as I think it's a good fit with Youngstown and Warren.
OH-16: Bill Johnson (Lime)
50% McCain, 47% Obama
This district could be called West Virginia West, because it shares similarities in voting patterns. It can be won by the right Democrat, so it's swing by definition in this area.
That breaks down to 5-5-6, which is a good fit for a swing state. Both parties are equal with safe seats and have plenty of opportunities.