Been years since I was there, but its a beautiful and unique country. Good taxi and train service just about anywhere you really want to go.
I flew BA out of London.
Check out some of the open air markets in Nairobi and hit as many of the restaurants you can. Stay at a named hotel, try to find one with 24 hour concierge, they tend to be the safer one.
You might want to check into an International credit card as well, they were accepted most all of the places we went and it cuts down on the cash you have to carry. Lot of places would also accept the Euro and the USD, not sure about now though.
Train stations and terminal stops are polluted with pickpockets just caution. Good place to hit the cash machines are inside the hotel lobbies, door hops tend to do a good job keeping the pickpockets out and they can't see you pocket the money, making you less of a target.
See Nairobi National Park, its huge and worth the visit.
Check with your cellphone provider to see if you can get coverage over there and roam without high fees.
But even if you can, once on the ground buy you a local prepaid cell from one of the shops at the airport and charge it up with a 100 minutes or so for a backup, cost you about $80 USD.
There were a few local travel agencies over there that were staffed by Brits, check in with them once on the ground and see if they will give you any advice.
They might even have a local tour group on the ground and invite you to tag along, they invited me and my ex-wife along on a day trip when we were there.
Find the local number for the Consular Services for American Citizens with the US Embassy and keep it for emergencies.
have fun and take lots of pics!