The country's cultural highlight, Dakar is home to beaches, boutique markets (I recommend Tilene Market), museums, excellent cafés and concert halls such as Thiossane, which is famous for playing host to Youssou N'Dour. Don't shy away from visiting your surroundings with a guide. They will be able to point out the sites you really shouldn't miss, such as the small beach, the city of Rufisque or Lac Rose (Lake Retba) which is located one hour away by road and is also the final stage of the Dakar Rally.
Another location to the North of Dakar which you really should not miss is Saint-Louis. Classed as a UNESCO World Heritage Site since 2000, the city is also known as the Venice of Africa. This is especially worth a visit if you are a jazz fan... If you can't make it to Casamance during your trip, the bird sanctuaries in the area such as Lengua de Barbarie National Park and Djoudj National Bird Sanctuary are sure to satisfy your curiosity for the local fauna.