Day 1:
If your flight is a late one (and most from the UK arrive in the afternoon/evening), check in to a Nairobi hotel. Choose the Fairmont Norfolk for a luxury option, or one like the Heron Hotel for a mid range price, 25 minutes from the airport.
Days 2-5:
Transfer to Guy and Julie Erskines Sanctuary Farm, two hours north of Nairobi, on the shores of Lake Naivasha. Stay three nights, either on a B+B basis or with dinner at the main house. Spend your days boating on the lake among hippo and cormorants, visiting Crescent Island and Hell's Gate, sightseeing in Naivasha, or getting a glimpse of the old settler life at the Naivasha Sailing Club or on the polo ground. Or ride on the farm amidst zebra and baby giraffe.
Days 5-8:

Transfer to Duma Camp in the Lemek Conservancy on the edge of the Masai Mara National Reserve. By road, the journey is through some intersting bush and takes about five hours. Alternatively transfer to by air - the airstrip is just a few miles from Duma Camp. Stay three nights, with an evening game drive when you arrive, and two game drives for each of the following days. Optionally, take a full day's game drive into the Lemek Conservancy and a trip into the Masai Mara National Reserve, though you will need to pay park fees. All meals included, only drinks extra. Duma is a wonderfully remote and unspoilt traditional bush camp - solar powered, six tents, run by Jennifer Ratcliff. Named after cheetah (Duma), you may see these, as well as lion, elephant, buffalo, hippo and, in the Mara, the white rhino.
Day 8:
Transfer back to Sanctuary Farm by road, for overnight before leaving for the airport (or the coast if you want a week on the beach). Alternatively transfer back to Nairobi by plane.