Khartoum's surroundings offer some of Sudan's most rewarding excursions, though "day trip" is a loose term here — distances are long and roads are rough.
Sabaloka Gorge is about 100 kilometres north of the city, where the Nile squeezes through a narrow granite canyon. You need a 4x4 to get there, and a guide helps. Along the way you pass small villages and the remains of an Ansar fort from the Mahdist period.
Meroe, roughly 320 kilometres northeast, is Sudan's most spectacular archaeological site — dozens of steep, narrow pyramids rising from the desert, built by the rulers of the Kingdom of Kush between 300 BC and 300 AD. It is too far for a comfortable day trip, but some travellers push through in a long day with an early start and a hired car.
Jebel Awlia Dam sits about 40 kilometres south of the city on the White Nile. The surrounding grasslands attract birdlife, and local fishermen sell fresh catches by the dam. It is the most accessible day trip from Khartoum and makes for a good picnic outing.
Dinder National Park, about 500 kilometres southeast near the Ethiopian border, is properly a multi-day expedition rather than a day trip. The park is open December to May and offers genuinely wild, unmanaged savannah — lions, giraffes, and buffalo in a landscape that sees very few visitors.