DD,
Tanzania is great for this type of safari. If you want to get a bit adventurous suggest you have a look at the Katavi Nat Park in SW Tanzania. I've been working in that area off & on for the past 20 yrs and it is a magic place. It is only a small park but is off the main tourist route and still relatively untouched. Used to be a game reserve. The only animals you won't see are rhino. Everything else is there in good numbers (especially cape buff & elephant) during the dry season. Several companies fly in from Dar and Tabora and there are tented camps with guided walks. Range of prices to cater for all budgets. Hunting is also available on several reserves in the region. I do agricultural work so I'm not tied up with any of the outfitters.

Pete (Australia)