If you only have a few weeks to travel in Africa and you have to pick one country, I highly recommend Tanzania. Tanzania was a major highlight of my Africa trip. It has the Serengeti, which is the best game park in Africa, the Ngorongoro Crater, Kilimanjaro and Zanzibar, the jewel of East Africa, so you can get your fix of wildlife, nature, beaches and cultures.
Avoid or limit your time in Dar Es Salaam, which is the jump off point to get to Zanzibar by boat. It’s a shit hole of a city (two of my friends, who were not traveling together, both got express kidnapped there. It is also a city where there are posters idolizing Osama bin Laden).
Tanzania, specifically Arusha (the jump off point to the Serengeti, Ngorongoro Crater and Kilimanjaro), is the best place to buy Tanzanite, a beautiful blue gemstone with a violet hue. Tanzanite can only be found in Tanzania, which is why it’s the best place to buy it, so you can avoid the mark-up in price.
If you want to hike Kilimanjaro, expect to pay around $2000US for the 8 days (I skipped it).
You’ll need your Yellow Fever vaccination and certificate to enter Zanzibar.
Swahili is the official language and you’ll easily learn a few words during your travels. You’ll also find that a lot of the words and names used in The Lion King are Swahili and have real meanings. Ie- Simba means lion and a sante sana means thank you very much. So when Rafiki, which means friend, says “a sante sana, squash banana”, he’s saying “thank you very much, squash banana”. And you’ll hear Hakuna Matata all the time, which means no worries. You’ll probably want to watch The Lion King before and after your trip.