Uganda is linked into the regional hostel network with some very nice little backpackers lodges tucked away here and there. In Kampala in particular look out for the Red Chilli which is a well fenced compound with a couple of old suburban houses converted into one of the nicest lodges in the region. It is also something of a travel entrepót for the local network so is a must if you are visiting Kampala.
There are others of course, with even more springing up all over the country. In keeping with vivid agricultural names Kampala also has a Blue Mango, and a creatively name Backpackers Lodge which cheerfully brings up the rear.
There are any number of camping opportunities within most of the national parks and most of the main backpackers lodges themselves. This is always the cheapest accommodation option, and is a pretty acceptable option in Uganda.