Hike in a comfortable, lightweight, breathable pair of shoes that you're able to wear for a long period of time. Depending on the terrain, you'll want a hiking boot or shoe, that will be able to withstand the territory and leave your feet feeling fine. If you're planning on hiking through water, you might want a shoe made of waterproof mesh and Gore-Tex. Remember, waterproof shoes can be hot though. Otherwise, choose a lightweight synthetic, trail running type shoe, that has openings of mesh throughout it, allowing your feet to breathe, while still protecting them.
Never wear a new pair of hiking shoes out for a long day of hiking. The last thing any hiker wants is blisters, knowing they still have miles to go before the hike is finished.