START RANT:
Please stop lumping all African countries together as if they're all one and the same! Africa has 54 countries and is larger than North America. The countries vary extremely - there is a huge range of cultures and geography across the massive continent.
Most countries in Africa are stable and safe... there are only a handful (out of 54) that are unstable/unsafe today! The problem is that the majority of the news stories that we read/see in the US about Africa are focused on the minority of countries that have issues. For example, the capital of Ghana is safer than any major city in the US. Really.
Uganda is very safe country now. Yes, it had a violent past, but it's in the past ... Idi Amin was kicked out in 1979. Kony hasn't been seen in Uganda in years (if he's still even alive; a photographer friend accompanied the Uganda Army hunting for him last year and they think he's dead).
My girlfriend and I have spent the last 1.5 years living in three countries in Africa, including 6 months living in Kampala, Uganda. We even bought a used RAV4 and drove about 5,500 miles all around the country (and it's a pretty small country) on weekends and holidays. We never worried about crime driving around the country; we did worry about getting into accidents - as in any developing country.
During the whole time in Uganda, my girlfriend and I never really had to worry about crime. We'd walk at night (albeit in the good parts of town) alone without fear. We'd drive anywhere anytime. My nephew visited for a few weeks and I didn't have to worry about his safety either.
It is a very safe country - just use your common sense as you would when traveling to any other country. Now, we live in Nairobi and it's called "Nairobbery" for a reason! There is a lot of crime here, so we are much more careful here than in Kampala. But, it's definitely not as bad as the perception that everyone has.
Uganda is a gorgeous country - the wildlife is amazing and the people are extremely nice. Yes, you can see more wildlife quickly in the Tanzanian Serengetti or the Kenyan Masai Mara, but you don't get the intimacy in those big over-touristed parks. For example, in Uganda, you can get within close proximity, on foot, of wild gorillas, chimpanzees, rhinos, giraffes, zebra, etc! Uganda is nicknamed "Pearl of Africa" for a reason. One of my biggest thrills was to do self-drives through the national parks and being about to really drive offroad looking for animals!
:END RANT
As for hotel recommendations in Kampala, it's important to know where the meetings will be as traffic can be pretty bad. Overall, the best areas to stay in are Kololo and Nakasero. The Serena is a gorgeous high end hotel; Emin Pasha is a nice boutique hotel. Kololo has an active nightlife with upscale restaurants, bars and a couple of clubs.
I highly recommend doing the gorilla tracking - it was one of the most memorable experiences of our lives. Feel free to ask questions!