There is tons of parking downtown. Also bussing in from Grandview wouldn't be bad if you don't feel like riding now and then.
I don't know any specifics about the Rhodes tower, but I wouldn't park my bike outside there for very long. Maybe one of the parking garages around there will have some bike racks inside, or you might be allowed to take the bike inside? There are a few gyms close by you could look into for showers if there are none at work. Metro Fitness is slightly closer than the Y and you could pretty much hop on and coast to the Rhodes from there. You'll have a pretty easy ride from Grandview though, especially once you get to the olentangy path. You can pace yourself there and may not even break a sweat/need a shower most days.