Wuse Market is the largest and most active market in Abuja, and the best place to see the city behaving like itself rather than like a government compound. The market covers an enormous area in Wuse Zone 1 and sells everything — fresh produce, dried goods, spices, fabric, electronics, shoes, and whatever else the city needs. It's crowded, noisy, and completely uninterested in tourists.
The food section is particularly good. There's an excellent range of Nigerian staples — suya (spiced grilled meat) from the stalls along the outer edge, abacha (African salad from the east), moi moi (steamed bean pudding), and various soups and stews from traders who have been in the same spot for years. For anyone who has been eating in the hotel restaurants of Maitama, spending an afternoon here is a useful corrective. Go on a weekday if you want to move without constantly being shoulder-to-shoulder.