If you’re on business and somebody else is paying, I would recommend the Serena hotel, which is central and rather nice in a traditional African style and has a good pool and super breakfasts. Ask them for a rate, don’t accept the first offer. There is a shortage of guests at the moment all over Africa.
If you’re paying, I guess you’ll need to trawl Tripadvisor.
Nairobi isn’t the same city it was when I first went there in 1995; you could drive round easily and have fun. It’s now just another grossly polluted and overcrowded African city with all the traffic jams, hassle, stress and dangers for the unwary. If you can choose your flights, try to arrive on a Saturday or Sunday so as to avoid the monster traffic jam down Mombasa Road. The airport is OK but Immigration and baggage are still in a temporary setup in a multi-storey car park, which works fine but might give you a bad impression.
You must be on business to be staying in the city for one whole week? PM me if you want further information.