There's some good advice here. I hope you find it useful for what is, I hope for you, a fantastic trip!
To this list I would like to add my standard bit of advice: Leave all electronic -- iPods, laptops, cell phones, etc -- devices safely stored back at home. You don't need them. Some people have taken this as some sort of safety warning, but the reasoning is more prosaic -- you're in someplace new and unfamiliar; you'll want to experience it with all five of your sense. No need to pollute your ears with the familiar when you're trying to discern where that lion's roar is coming from.
The word "safari", in Swahili, means "journey"; it has nothing to do with animals. Someone "on safari" is away and unobtainable and out of touch.
Two weeks is too short in my opinion. With the amount of wildlife activity going on, you could fill up two weeks without breaking a sweat. I'm going to suggest four-to-six weeks to a.) fulfill some of your dreams while this trip and b.) provide slightly more than a cursory impact on these orphans' lives.
I'll second the thought of bringing gifts. In my brief time in Kenya, the people were just as interested in where I came from. I'd suggest bringing some pictures of your home area to show off what life is like. You can compare and contrast, and be prepared to answer dozens of questions.
I was going to recommend The Carnivore in Nairobi, but it's now against Kenyan law to eat game. South Africa doesn't yet have this concern, but that's a different story. The most exotic thing you'll find nowadays -- from what I've read -- is ostrich. Gone are the days of impala, antelope, crocodile, etc.
Everything goodeknight mentioned, I agree with. To that I would add: day & truck safaris suck. They amount to so many trucks & guides swooping from water hole to water hole attempting to get you the quickest views of the Big Five.
It's not uncommon for fifteen trucks to be parked around any given waterhole.
Do the camping safari. I'd tell you to look into a horseback safari -- I did one in the Okavango Delta -- but I don't think they have them in Kenya. Too many big cats, and it's forbidden to get out of the truck because of this. Still, it might be worth looking into.
And while they're no specific dates, you'll be arriving smack dab in the middle of calving season. There's bound to be scads of animals about. Be sure to ask the difference between a reticulated and maasai giraffe.
I am, unfortunately, unfamiliar with Bungoma. I was glancing at my map, so I know it's in Eastern Kenya, but that's about it. The good thing, however, is it's very near to Uganda. Uganda, as you might know, is prime gorilla viewing territory. The city of Jinja, on the banks of Lake Victoria, has some spectacular whitewater rafting on the White Nile.
There are far cheaper local operators out there, but I have always wanted to try out Abercrombie & Kent's Mobile Camping Safari
. Then check out the prices
to see why I've never tried them out! I could spend six months on the continent for that kind of money.