The cheapest (and safest) option in East Africa would be the tours with company's like Acacia that do tours in four-wheel-drive buses/trucks and camping in tents most nights.
We went on one in 2003 that left from Nairobi then visited the Masai Mara,Lake Navasha,Amboseli,Ngoro Ngoro Crater and 3 nights on Zanzibar then back to Nairobi.
We had a great time. The wildlife was amazing - 23 lions in the first afternoon at Masai Mara including a group of females hunting.
Zanzibar was an Amazing place and well worth visiting if you can.
Asia is a very BIG place - anywhere you have in mind ?? North Vietnam is my favourite at the moment including Hanoi, Halong Bay and Sapa.
Look forward to your Photo's.