There are several versions of Morris (aka Mills and Merrills) in the App Store, but I'm perfectly happy with Mills and More, from Antitalent Game Studio. It has simple touch controls for placing and moving markers, and clean, appealing graphics, with markers that look like Go pieces.
The Lite version includes the basic Nine Men's Morris in 1 and 2-player modes, with three levels of articifical intelligence and Bluetooth support.
The registered version adds Three Men's Morris and Six Men's Morris, and the developer is promising Twelve Man's Morris in a future update. The "flying" run can be toggled on or off.
Give the Lite version a try. If you like abstract strategy games, you might find this an appealing alternative.