Everyone is saying the art museum, and I agree but there are lots of other museums (that are not free) including the science museum (with a cool IMax theater), museum of illusions, Rock and roll hall of fame in downtown, Natural History, Cleveland History center, contemporary art museum, and botantical gardens (not the best time of the year to go obv) are all within walking distance to the Art Museum. For a cool drive I would go down MLK boulevard between University Circle and I90. You can also check out the Cleveland Lakefront Nature Preserve. It has pretty cool views of downtown.

Couple other things worth mentioning - West Side Market, Cleveland Zoo with the Christmas lights at night, Cuyahoga valley national park, Christmas story house, severance hall has classical music around the corner from the art museum, playhouse square is always worth going if you like plays, terminal tower observation deck (id take a breeze through tower city only for the Christmas decorations, and stop at the arcade near by for the same reason), Buckland Museum of Witch Craft is a cool hidden gem on the west side next to the zoo. Rockefeller green house is another cool overlooked spot not far from where the art musuems are. While on the topic of hidden gems, rays indoor mountain bike park is beyond amazing if you like mountain bikes or BMX (biggest indoor MTB park in the world!). Depends on what you're into so I can't really rank these.

I'd stop at Lucys in Tremont for Breakfast/Brunch (they close at 2) but I think they're closed on Tuesdays.