Miriam,
We spent 3 weeks in Kenya & Tanzania in 1984 when they were safe & South Africa was not. Tanzania had just opened up to the west & some of the lodges that were once beautiful had been neglected under communist rule. We spent all our time on safari & no time in the big cities. The Ngorongoro crater & the Serengeti are amazing. We went in March at the height of the wildebeest migration. We saw everything plus a thrilling lion kill.
You will have a wonderful time & great animal viewing.
Best of Luck, Jackie