Bamako isn't packed with formal sights, but what it has is worth your time. The National Museum is one of the best in West Africa, covering the civilizations of the Niger Valley with real depth. The Plateau Viewpoint gives a good sense of the scale of the place — the river, the hills, the sprawl below.
The Grand Mosque in the Bozola neighbourhood is worth seeing for its architecture and the Friday congregation that spills into the surrounding streets. The Grand Marché — vast, chaotic, and genuinely good — is where you'll find Malian bogolan cloth and the best street food in the city. The Palais de la Culture is the place to hear live Malian music in a proper setting.
At dusk, walk across the Pont des Martyrs for views of the Niger and the pirogues working the water. The Parc Zoologique et Botanique provides rare green space in the city and is worth an hour with or without children.