Parking garages don't have to be eyesores. They can be rather impressive architectural additions to a city.* For example:
http://www.ArchitectureWeek.com/2006/1115/design_1-1.html
http://www.ArchitectureWeek.com/2005/1012/building_1-1.html
http://www.archnewsnow.com/features/Feature107.htm
http://www.slate.com/id/2179373/
So long as the car remains the predominant way for commuters to get into and out of the center city, parking will be a necessary evil that consumes otherwise valuable space. Until the community gets serious about mass transit, it really would be a good idea to offer incentives for the owners of those private lots to seek and develop new parking garage designs (maybe some as dual-use buildings) that have positive economic and environmental impact. I agree with the OP that those lots are good spots for development and are somewhat discordant with the new Short North, but the need for parking remains. I think it's another example of how the "Old Columbus/New Columbus" tension is more of an opportunity than a conflict. It also relates to the recent thread where it was suggested that Columbus's lack of skyscrapers equates to a dearth of architectural identity. I don't agree at all that adding tall, mostly redundant office buildings to the skyline is the way for a changing city like ours to achieve recognition for being modern and open to architectural innovation. It will be small, smart, thoughtful, and tailored projects that solve relatively mundane problems like parking that can put the city on that cutting edge.
*Just to be clear, I'm being totally sincere, here. I wouldn't want to waste anyone's time by eliciting accusations that I'm perpetrating some king of a ruse.