My favorite places to stay...
I've stayed in tons of places in Uganda, but my all time favorite is Jacana Lodge in Queen Elizabeth National Park. It is beauitfully constructed to blend into the surrounding forestry, overlooks a crater lake, and is extremely tranquil and relaxing. Simply comfortable and relaxing, with great food and service. One drawback - although Jacana is surrounded by forests with Colobus monkeys and Baboons, the 'real' safari animals are a bumpy 45 minute drive to the main entrance of QENP. If you want to be closer to the 'action' then Mweya Lodge might be the better bet. Jacana is roughly $110/night including all meals. Check it out at http://www.innsofuganda.com/jacana.html
In Kampala... the new best hotel is the Emin Pasha (which it should be at $220/night). It is in a somewhat isolated section on Nakasero Hill, so a car or using taxis would be preferable. See it at http://www.eminpasha.com/
The Sheraton, of course, is very nice, but not as nice as the Emin Pasha. The Nile Hotel is currently undergoing redevelopment and will be re-christened the Kampala Serena hotel in June 2006. This should rival the Emin Pasha. It is in a great, fairly central location.
In Kampala I've stayed at the Sheraton, Mosa Court Apartments, Nile Hotel (to become the Kampala Serena), Fairway Hotel, and Hotel Equatoria (all in the $70-150 range). My wife and I stayed at the Sheraton in 2001 and she - new to Africa - found the pool to be a great place to unwind after a long, hot day. If you're staying for several weeks I'd highly recommend the Mosa Court apartments just down from the Sheraton... great location with an apartment-like feel, including furnished kitchen.
I haven't stayed at the Blue Mango, but from my meals there it looks like a nice, cheaper option. OUTSIDE OF KAMPALA:
In Entebbe, the best, cheap place to stay is the Bagonga Convent (yes, nuns are there but it is very nice, clean, quiet, and relatively inexpensive - $25/person/night). Three $100 plus places are Botanical Beach Hotel which has a beautiful view of Lake Victoria, the Resort Beach Hotel (Never sayed there), and the Lake Victoria Hotel with good food and a great swimming pool that was frequented by skinny-dipping Peace Corps Volunteers!!! I like the Lake Vic for my 1st night in Uganda since it is so close to the airport.
In Mbarara my new favorite is the Marble Arch. I stayed there in 2005 and was rather impressed... clean, somewhat cheap, and good food. I've also stayed at the Lake View Hotel, the Pelikan Hotel and Riheka Guest House. All are nice, but the last 2 are cheaper.
In Kabale I always stayed in the Visitour's Hotel (cheap - I think around $10)). It was fairly decent. Nore expensive options are the White Horse Inn and Highland Inn (around $50-60). Both are quite comfortable, but for the money White Horse wins.
One must see place while in Kabale is LAKE BUNYONYI. It is absolutely beautiful. Hire a canoe over to BUSHARA ISLAND. If you can, I highly recommend camping on this island. The Church of Uganda has set up several permanent tents with beds for $35/night (the clean outhouse is a short walk away). This island is a true treasure, and the cooks make incredible crayfish masala. http://www.acts.ca/lbdc/bushara/
At Bwindi, I stayed with a Peace Corps Volunteer, so I don't have any advice. I know there are inexpensive campgrounds and expensive luxury camps, but I really can't make a recommendation. Sorry.
As you can see, there are many great places to stay and the choices are improving every year. Enjoy the warm hospitality, great food, and friendly service.