I'll be in Chicago for a two day business trip in late June -- my first to the city. I can't imagine coming to Chicago and not trying some authentic Chicago pizza - plus I love a good pizza. I'm staying at the Four Seasons on East Delaware and want to try both deep dish and thin crust Chicago pizza. I'd love suggestions for great Chicago deep dish and thin pizza. Places within walking distance of the Four Seasons or a short (20 min.) cab ride would be especially appreciated.

Thanks!