Hello Neej and welcome to Travelblog!
I did this trip back in 2008 and really enjoyed East Africa, a fabulous part of the world to travel in.
However, the best activities I saw are all going to cost you a lot of money, such as the the gorillas (minimum $500 for the visitor pass) or a safari in Kenya/Tanzania. At that time of year, you are best to head to the Serengeti and Ngorongoro Crater in Tanzania.
It is possible to do a safari on the cheap, but the best experience is undoubtedly the more exclusive offerings in specially designed vehicles - less crowded and greater viewing options. I've done safaris in all manner of vehicles and the specialised ones are easily the best for a safari.
Of the countries you mention, I felt that the safest was Rwanda, but that is not to say that the others are dangerous. Basically, you'll need to modify your evening social patterns. I am a solo male traveller and I wouldn't go anywhere more than an hour after sunset. Since the social side of travel (i.e. mixing with other travellers) is unimportant to me, it was easy to stay in my room each night and sort through photos.
I should mention that April is rainy month in Kenya, so many of the parks are closed at that time. I doubt that Kenya will see the inter-tribal violence that marked the 2008 election (the 2010 referendum was peaceful) but there have been rumblings about poll boycotts in Mombasa - and you have already noticed these.
Uganda is becoming a bit of an adventure destination, and the area around Jinka is home to all manner of activities such as white water rafting.
I did not travel to Zanzibar, but I have heard mostly good things about the island. For my fix of Swahili culture I headed to Lamu in Kenya, but last year it succumbed to violence from nearby Somalia, and general advice was to stay away. However, that may have resolved itself by now. If it is safe, I'd recommend a visit, the Old Town of Lamu is very interesting.
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