Everyone I know who has dared to wear heels for the whole day has regretted the decision for a week or more afterward! If you'll be dancing at the Expo or at PFF on Saturday evening, wear dance shoes, then change into comfortable shoes for the parks. There are all kinds of comfortable, flat shoes that can look fine/cute with dapper outfits, e.g. saddle shoes, keds in all colors (and white keds can be dyed to match an outfit), ballet flats by various makers (some are surprisingly supportive, like Crocs), mary jane styles (again, some are surpisingly supportive), TOMS (all colors! check the bridal TOMS section on the website), ankle boots for certain period looks, etc. Whichever shoes you pick, make sure to break them in before Dapper Day Weekend and to wear peds or socks (bring spares) to prevent blisters.