Giant Redwoods, the kind you see in California and on the west coast are borderline hardy in USDA hardiness zone 6. Some of Ohio is in that zone, so you'll have to consult a hardiness map to check your area.
You can try Dawn redwood (Metasequoia glyptostoboides), they are hardy in zone 5 (I think all of Ohio is either 5 or 6). They are truly beautiful, I grew one at my parents house outside of Detroit. People used to stop, to ask them what it was. They are deciduous (drop their needles in the winter), so don't be alarmed when the tree goes bare. The bark is also an amazing feature.
Similar trees include Bald Cypress (Taxodium distichum) and Larch (Larix decidua). All of them are nice and different.
I hope you find one you like.
I am a professional horticulturist