I just returned from climbing Kili and transferred through Nairobi airport. Since there is conflicting advice about the Nairobi airport, I want to provide a real-time update.
First, getting my bags. Since I flew in on an evening flight and was flying out in the morning to TZ, I wanted to get my bag and stay in the "Sleep-n-shower" in the airport. Contrary to advice given at the airport, there are at least 2 methods to get your bag - 1) pay a "porter" that is standing by the passport control to get your bag or 2) give your passport to one of the "official" looking gentlemen standing by passport control and retrieve your own bag and walk back to passport control and retrieve your passport. Neither method comes with a great sense of comfort, but I chose the former.
I paid a porter a couple of USD's, gave him my claim ticket, and said there would be more USD's when he returned. After 15 minutes, here he comes walking through passport control with my bag. USD's well spent in my book. As I was waiting for my bag, I saw a guy deploy technique #2 - gave his passport to one of the better dressed "officials," he walked down to baggage claim, and about the same time as my chap returned he walked back to passport control and after a brief discussion, retrieved his passport.
Why did I choose #1? I NEVER surrender my passport without a really good reason. But that's me. Choose for yourself.
Second, staying at the "Sleep-n-shower." Nairobi airport has a 14 room sleeping room place down by Gate 3 in the international terminal. After I retrieved my bags, I walked down the hall, down the stairs, and to the double doors signed "sleep-n-shower." You can't miss it. It was very basic, the prices are as previously posted on the forum, and a bed. It was hot and humid, but at least a bed and toilet. The showers are interesting, and make sure you ask for towel, flip flops, and how to turn on the hot water.
Third, nobody at the airport really knows what is going on. You will hear conflicting answers from anyone you talk to. Where do I check in? How do I check my bag? Where is such-n-such? I heard different gate assignments over the PA for my flight over the course of an hour. Folks told me flat out wrong answers to my questions, and fortunately, I didn't believe them. Get there early, get in line early, and be observant.