There is a lot of great literature based in Uganda, written both by Ugandans and non-Ugandans: These include:
Abyssinian Chronicles (Moses Isegawa), Aboke Girls (Els de Temmerman), Kintu (Jennifer Nansubuga Makumbi), Song of Lawino & Song of Ocol (Okot p'Bitek), Child Soldier (China Keitetsi), Last King of Scotland (Giles Foden), and The Worst Date Ever (Jane Bussman).
There are so many amazing African based novels by excellent African writers. In no particular order, these are a few to get you started:
Things Fall Apart & No Longer At Ease (Chinua Achebe - and so many of his other novels), Half A Yellow Sun (Chimamanda Ngozi Adichee), Purple Hibiscus (Chimamanda Ngozi Adichee), The Boy Who Harnessed the Wind (William Kamkwamba & Bryan Mealer), The Devil That Danced on Water (Aminatta Forna), Lyrics Alley (Leila Aboulela), The River Between (Ngugi wa Thiong'o), July's People (Nadine Gordimer), Disgrace (J.M. Coetzee), The Joys of Motherhood (Buchi Emecheta), and The Famished Road (Ben Okri).
Other fictional novels set in the region include:
Poisonwood Bible (Barbara Kingsolver), We Wish to Inform You That Tomorrow We Will Be Killed with Our Families (Philip Gourevitch), A Sunday at the Pool in Kigali (Gil Courtemanche), The Constant Gardener (John le Carre); The Shadow of the Sun (Ryszard Kapuscinski), Blood River (Tim Butcher), and A Good Man in Africa (William Boyd).
Uganda has a very strong music culture with a lot of popular artists becming more renowned both across the continent and throughout the world. Artists you can check out include: Joel Sebunjo (who supports the work of LBA), Bobi Wine, Radio & Weasal, Bebe Cool, Chameleone, Juliana, Wilson Bugembe, GNL Zamba, Raga Dee, Jamal, Cindy, Irene Nambiru, Lilian Mbabazi, Salome, Sandra Suubi, Naava Grey, Peter Miles, Maurice Kirya, Afrigo Band, Eagles Productions, Qwela Band, Isaiah Katumwa, Desire Luzinda, Toniks, Blu 3, Grace Nakimera, Aziz Azion.
Also check out Kadodi - the traditional music from the Mbale region.
Uganda featuring on the big screen: The Last King of Scotland. Top Gear also had two very entertaining episodes when they filmed in Uganda (get them on Youtube); Close to home but not quite Uganda: The Constant Gardener, Hotel Rwanda, A Sunday in Kigali, Blood River, Blood Diamond, Desert Flower, Virunga and, going back a few more years, Out of Africa