If you can't or don't want to go along with some of the suggested treatments in this link or if they are to no avail and you can't get to a position where you can practice an art barefoot then I too recommend many of the kung fu systems, or a reality based programme such as krav maga or a jeet kun do/JKD club where they train in sparring and on the bags etc wearing shoes.
I took wing chun for a couple of years alongside my karate for interest and to get some of the system's ideas into my own style and we always warmed up, trained and sparred wearing those traditonal, iconoclastic slip on black shoes/slippers.
It's hard to know what to suggest without knowing what you want the style for. If you want something you can apply 'relatively' quickly to street/SD situations then krav maga or JKD would be the way to go IMO. Nothing against the principles of wing chun or shaolin KF but in my experience (albeit limited) these more traditional arts progress slower through the technique applications and preparation for full on fighting - so if you are after something more long term with a rich content then maybe these would be more for you; also these styles are generally very good for conditioning in flexibility, suppleness and cardio from day one.
If you are after a ring sport with great kicking skills, then I would say Savate - this is a French originating art but I don't know if there's any chance a club would be anywhere near you as tends to be quite rare outside of Europe - but there are clubs and trainers around. Also on that note, if you are after a style for fitness/conditioning and don't need to focus on leg attacks and grappling then go for boxing - can't beat that really within those parameters and generally there's a club or old trainer with a speed ball in a dungeon gym in most places.