not sure what sort of recommendation you're looking for but October is a good time in Kenya and Tanzania - the rainy season starts in November (usually); before that it's dry, animals have to come to water holes to drink and are therefore easier to see. The cheapest way of doing this is usually some sort of package from someone like Thomsons involving a stay on the Kenya coast plus a few days at a safari reserve inland.
http://www.thomson.co...win-centres-east.html
If you can pay more, all sorts of tailormade options are available. A few years ago we went to a private reserve in South Africa followed by a stay at a resort in Mozambique; the next year it was safari in Tanzania (Ngorongoro and Serengeti) followed by days on Zanzibar. We booked through Theobald Barber
http://www.theobaldbarber.com/
I couldn't call them cheap, though.