Uganda has great range of ecosystems and wildlife, from classic African safaris in the savanna, to trekking for gorillas and chimpanzees in the jungle..
I explored Uganda on a month long trip in October-November 2019.
If you don't want to be on a tour and stuck with other people, and you want to have the freedom to do your own thing when you want and at your own pace, then you might consider hiring a car. It is possible in Uganda, with various companies, including Self Drive Uganda (this is who I used). In the office, Joy can also organize gorilla trekking permits.
Be warned, it is not the sealed roads and nice road stop cafes of South Africa. The roads in Uganda are rough! especially in the wet season, and even the 'main' roads connecting the towns. There is continual road construction and lots of very slow trucks that will drive in the middle of the road and not make it easy to pass safely. But it makes you appreciate the sealed roads when you get on them.
Finding your way around can be tricky sometimes; Google Maps steered me the wrong way several frustrating times (sometimes the 'shorter way' is not that, and downright dangerous), navigate using old-fashioned maps in conjunction with electronic. The RAV 4 is great, but next time, I might consider a landcruiser, as it has higher clearance for some of the lumps in the road, and the higher seating in the car make finding wildlife easier in the wet season tall grass.
Uganda has a good range of national parks that reflect that different habitats. They mostly have a wide array of accommodations, including basic and cheap to luxury, with mostly mid-range lodges; the latter cater to the small group tours. Getting a good lodge is vital of course. The most important aspect of this is location. It is usually preferable to stay at a place within the national park. However, this also means you have to pay the entry fee every day and you may not be able to walk around much unguided.
Some of the best spots are roads that actually pass through national parks and reserves.
The most famous national park in Uganda is probably Bwindi Impenetrable.
One of the most famous national parks is Kibale. This has the best primate watching in the world. To see some birds and good primates adjacent to the national park, there is the community run Bigodi Wetlands. You can stay in the rainforest in the national park at Primate Lodge, or just outside at the pretty Isunga Lodge.
Another famous national park in Uganda is Murchison Falls National Park. One of the most popular actvities there are the cruises up to Murchison Falls.
Queen Elizabeth National park is one of the more accessible and heavily visited protected areas in Uganda, and has a variety of habitats and wildlife. Here you can do the Kazinga Channel cruise.
Uganda has wide open savannas, closed canopy rainforest, rivers and lakes. It also has high mountains, and even though the country is located on the equator, there is snow and ice on top of these mountains. They are the Rwenzori Mountains , and I stayed at Ruboni Camp.
One of the closest national parks to the big cities of Kampala and Entebbe (although it is still a long half day drive), is Lake Mburo National Park.