The most memorable place I've ever visited is Tanzania. Growing up, one of my favorite things to do was watch nature shows on the Discovery Channel. The best ones were always about the Serengeti. Getting myself to Africa to see lions, cheetahs, elephants, giraffes (well, all the animals, really) had always been a life goal. Can confirm that it's so much cooler in real life than it is on TV.
My favorite place to go running is Hyde Park in London. It has enough paths that you'll always find a new route, and the surroundings aren't too shabby either. You can pass by meadows, ponds, and Kensington Palace all on the same run!
The one thing I won't travel without is my camera! Photos are some of the best souvenirs and I love looking back on all the memories once I get home.