"There was never another time like that first time in Africa," recalls Harry Street, Hemingway's narrator in The Snows of Kilimanjaro. Whether it's your first or 10th time on the continent, there certainly was never another place like Tanzania. It's one of those corners of the planet where you can still feel you're living a storybook adventure. Picture sitting by a jungle campfire, boots propped up on a battered leather safari case, sipping a sundowner as someone describes a run-in with a lioness and her cubs. Or later, as you drift off in your comfortable canvas tent, listening to the night sounds of the jungle and wondering whether tomorrow's first encounter will be with zebras or elephants.

Tanzania is home to some of the most renowned game reserves in Africa. And of all the wildlife experiences on offer, undoubtedly the most spectacular is the migration, between November and February, of two million wildebeests across the Serengeti plain. You can follow their exodus camping in luxury yurts – an eccentric but ideal cross between the tents of Masai warriors and the portable huts of Mongolian nomads. Or enjoy a more traditional stay in an acclaimed lodge overlooking Ngorongoro Crater.

Further south is Selous, Africa's largest reserve, where we can create a private safari on foot, by four-wheel drive or even by boat. Enjoy evening dips in natural hot springs after days of tracking black rhinos and other exotic game – or, if you like historical oddities, exploring trenches dug by German and British troops during WWI.

Then there's Kilimanjaro, Africa's highest peak at 19,330 feet, yet eminently climbable for active travellers who are reasonably fit. The hike is all about pacing yourself, testing your limits a little and experiencing the thrill of a once-in-a-lifetime achievement. Reaching the summit truly is a glorious feeling – and as you watch the sun rise over the surrounding country, even the simple act of sipping a cup of tea has an immediacy you'll never forget. Our experienced mountain guides and porters make this challenge as attainable as you'd wish it to be.

And after you've climbed to the "Roof of Africa," where better to unwind than on Zanzibar, the legendary spice island off Tanzania's eastern coast? With its ancient and colonial history, vibrant Arab culture, fascinating architecture, white-sand beaches and incredible diving in the Indian Ocean, it's a wonderful final chapter to your African adventure.