A safari is usually the reason people come and rarely the whole trip. Here's what's genuinely worth the extra days.
Zanzibar
The obvious one, and it earns it. Stone Town is a UNESCO World Heritage site and an afternoon getting lost in its alleys is the best way to see it. The east and north coasts have the beaches, the Jozani forest has red colobus monkeys found nowhere else, and the diving and snorkelling are excellent. Three or four nights after a safari is the classic combination and it works because the pace is the exact opposite. There's more under Zanzibar.
Kilimanjaro, without climbing it
You don't have to go to the top. Day hikes into the rainforest on the lower slopes are beautiful and need no preparation, and the mountain pages cover the full climb if you change your mind. The coffee farms on the southern slopes around Moshi do half-day visits that take you from the tree to the cup, and they're far better than they sound.
A day trip from Arusha
If you've got a spare day at either end, Arusha National Park has giraffe, colobus and a walking safari option, and Lake Duluti and the Materuni waterfall both make easy half-days. We keep a list under day trips.
Lake Natron and the Rift Valley
Harsh, strange and unlike anywhere else: a soda lake under the active volcano Ol Doinyo Lengai, with flamingos breeding on it and a walk up a gorge to a waterfall. It's a rough drive and it's for people who want landscape rather than comfort.
Chimpanzees in the west
Mahale and Gombe, on the shore of Lake Tanganyika. Remote, expensive, flight-only, and one of the great wildlife experiences in Africa. Trekking up a forested mountain to sit with habituated chimpanzees is nothing like a game drive. Budget properly and plan around flight days.
Cultural visits, done honestly
Maasai villages, Hadzabe and Datoga communities near Lake Eyasi, Chagga villages on Kilimanjaro's slopes. These vary enormously: some are real exchanges that genuinely benefit the community, others are a performance for a car park. Ask who gets paid and how, ask whether you'll be asked to buy anything, and be willing to skip it if the answers are vague.
How many extra days
Three or four for Zanzibar, one either side for Arusha and its day trips, two for Lake Natron, and a week of its own for the west. Pick one. Trying to do three of them is how a good trip turns into a tour of airports.
Mafia and Pemba, if you want quiet
Zanzibar has neighbours. Pemba is greener, hillier and far less visited, with superb diving on its walls. Mafia, further south, has a marine park and is one of the more reliable places in the world to snorkel with whale sharks in season. Both take more arranging and reward it with beaches that have nobody on them.