Why are my feet stiff in the morning, but get better as the day goes on?

Osteoarthritis. Pain and stiffness in the am upon arising are usually due to osteoarthritic changes to the bones of your feet from trauma or aging. Often the discomfort will lessen with movement, and return to plague you then following morning. I would suggest a podiatric consultation to determine the exact cause, and possible treatments, which might include oral nsaia, topical nsaia, or orthotics.
Feet stiffness. Sounds like you might have some arthritis. Would get them evaluated by a doctor and get them xrayed.