There's basically 3 hikes up there: easy is Timber Creek Overlook, about half a mile. Intermediate is Taylor Creek and you see 2 old cabins. Hard is Kolob Arch. Your time and abilities will determine which is for you. There's also an unofficial hike up south fork of Taylor Creek or you can go outside the park up Kannara Creek but it might be a little cold this time of year.
Kolob Arch is the neatest, but takes most people all day. If you run it, it only takes 3 hours though.