At 900 sq km, Niokolo-Koba is Senegal's largest national park. It's listed as a World Heritage Site in danger, as park resources barely suffice to adequately protect the remaining animals (including elephants, lions, warthogs and various monkey and antelope species). The park's official opening season is 15 December to 30 April. It's open at other times, but is largely inaccessible during the wet season (June to September).
You can also explore the park by 4WD (indeed you'll need one just to be allowed entrance into the park), though sightings of the rare mammals are far from guaranteed. The entrance fee gives you access for 24 hours. You get your obligatory guide at the entrance gate.
The trail from Tambacounda to Kédougou passes through the Niokolo-Koba National Park, the country's largest national park. Here, you can see wild animals before setting off on a boat trip on the Gambia River. The best time to visit this part of the country is during the dry season.