Well, since you are on the Cleveland forum, I will suggest Cleveland. It also makes sense though, because the best hotels in Ohio are in Cleveland as well as the most popular tourist attractions and in my opinion the best restaurants. You could start off with a fun tour on Lolley the Trolley or a romantic tour on horse drawn carriage.
I'm not sure what your budget is, but the nicest hotels in Cleveland are the Ritz-Carlton and Renaissance Hotel. The Hyatt downtown and the Glidden House Inn in University Circle might also be nice. A lot of the hotels offer various entertainment and attraction packages that would be worth considering.
Downtown the Rock and Roll Hall of Fame museum is one of the most popular attractions in the city, and an amazing example of modern architecture. Playhouse Square is large collection of theaters (second in size only to Broadway in New York) and perhaps worth a visit. Terminal Tower is a beautiful complex that includes some decent shops and restaurants, but is a must-see attraction in Cleveland. You can walk from Tower City to these other must-see things to see in Cleveland are Public Square, Old Arcade, Civic Center, and E.9th Pier.
University Circle is the second major hub in Cleveland where the cultural, educational and medical institutions are primarily located. These institutions surround a beautiful lagoon and park called Wade Lagoon. The Museum of Art is closed due to construction, but the Botanical Gardens nearby are certainly worth a visit. An evening at the world famous Cleveland Orchestra (the highest rated in the country) at beautiful Severance Hall in University Circle would be excellent idea.
For cool nightlife and dining districts, you should start at the Warehouse District downtown just west of Public Square along W.6th Street. The Metropolitan Café is very popular, good location, great atmosphere, and simply a good place to start for dinner in the Warehouse District. From there you can go to cool lounges like Mercury Lounge, Sunset Lounge, or D’Vine Wine Bar. Sushi Rock and XO are other great restaurant and bar, and very popular. The other great thing about the Warehouse District is during warmer months there are great outdoor sidewalk patios.
East Fourth and Euclid is an emerging entertainment district just east of Public Square. Dinner at Vivo’s would be great, and then you could see a show at the House of Blues or comedy at Pickwick and Frolic’s across the street from Vivo’s.
Cool daytime districts for lunch and unique shops and galleries you should start in Ohio City on W.25th Street just west of downtown. Start at the Westside Market (a must-see European market when in Cleveland), and continue on W.25th street to Opa!- a tiny romantic restaurant for lunch. The Great Lakes Brewing Co. is another popular place in the neighborhood and they offer tours.
Little Italy just East of University Circle is another must. You could pick any of the restaurants here on Mayfield Rd., and browse a lot of galleries and boutiques here. It has a lot of character, and is pretty romantic.
Other Romantic restaurants to consider would be Ponte Vecchio on the west bank of the Cuyahoga River with beautiful views of the skyline, San Souci restaurant off the beautiful Renaissance Hotel lobby with beautiful views of Public Square, and Severance Restaurant at Severance Hall with great views of Wade Lagoon would be nice too.
Congratulations and enjoy your Honeymoon! I hope you consider Cleveland if you are planning to Honeymoon in Ohio.