It depends on where you start. Lake Mburo National Park is the closest real safari destination to Kampala and Entebbe.
The park lies about 4 to 5 hours southwest of the city. Several lodges around the park offer excellent day safaris, and these are definitely worth doing. In a single game drive and boat trip, you can see an impressive variety of wildlife. Expect zebras, giraffes, buffaloes, hippos, impalas, topis, bushbucks, waterbucks, and plenty of birds.
But what if you start and finish in Kampala or Entebbe on the same day? Honestly, we would not recommend it. The return journey alone can take more than 10 hours. That leaves only a few hours inside the park. And unfortunately, those hours are usually in the middle of the day. That is when the sun is at its hottest. The animals are less active. And the light is not ideal for photography.
So, while a 1-day safari from Kampala or Entebbe is possible, it involves a lot of driving for a very short safari experience. If you can, spend at least one night near the park. You will enjoy better wildlife viewing, a more relaxed pace, and a much more rewarding safari overall.