Music, boat rides, food. Maybe you'll be able to see Bulingugwe Island.
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Munyonyo Commonwealth Resort
Speke is a very fancy resort with a marina, gardens, a pool, beach, gym and squash courts. There is a restaurant in the resort with a large selection of food and drinks for everyone. For entertainment, horse riding is available with guides taking you around the resort, and boat drivers can take you out into the lake and back to experience the breeze and take scenic pictures. The resort also has a lot of walking areas, perfect for romantic endeavours.
Mengo Palace
Royal compound of the Kabaka/king. Historically significant place, but not much to see. The original Lubiri was destroyed in 1966 when Milton Obote took power and the Kabaka fled the country. To the west along the Lubiri Ring Road is Kabaka's Lake, a man-made body of water ordered by King Mwanga of Buganda that you can walk around or canoe in, but, whew-wee, there's a little bit of a stink problem from sewage going directly into it. Cost to enter the lake area is USh 500.
A longstanding Hindu temple in Kampala where the emphasis is on Lord Shiva.
Uganda National Cultural Centre
A big cultural centre with a theatre that also hosts dance shows/lessons/events, comedy, films, concerts, jam sessions, improv and discussion nights. The current program can be found at the entrance or online on social media or website. Every Monday there's a music night with live music from artists on stage. There is a restaurant located inside the venue, with a wide range of food and drinks. There's also a library, a restaurant and a large African Crafts Village with dozens of shops selling souvenirs, crafts, and also some stuff that is more artsy than all the stuff you can find everywhere else.