Well downtown Cleveland- very near the lake- you will find several nice romantic hotels like the Ritz, Renaissance, or Hyatt. In addition they are all near excellent restaurants and classy nightlife establishments like on W.6th or E.4th. I think any of these hotels would make a nice honeymoon experience. You could do a number of things like visit downtown attractions like the Rock Hall, Tower City, Playhouse Square, West Side Market, Lolly the Trolley Tours, or the Goodtime III boat tours. Don't forget that excellent museums and cultural institutions are located in University Circle, which is the cultural hub of the city and the institutions surround a beautiful lagoon and park. Nearby University Circle is Little Italy which is the perfect spot and ambiance for a romantic lunch or dinner.
If you really wanted to be close to the lake in Cleveland, then Edgewater Estates would be a nice consideration. It is a bed and breakfast in a historic mansion in one of Cleveland's most prestigeous and beautiful neighborhoods called Edgewater. It is also within a minutes walk of Edgewater State Park which boasts ample park grounds, beaches, and downtown views.
Outside of Cleveland but within an hour drive or so are the Lake Erie Islands in the Sandusky area to the west or Geneva-on-the-Lake to the east. Both of these areas boast lots of cottage rentals and bed and breakfasts with lakefront views and relaxing things to do. You might find these places more relaxing and laid back than downtown Cleveland, but not quite as classy.
Congratulations, and enjoy your honeymoon!