When you travel, you experience something completely different. You move through different streets, trails, homes, places; you meet new people who see the world through different eyes. Travel shakes us up and sets us down somewhere new.
If you want to be innovative, then, you must travel.
Innovation comes from creating brand new ideas or combining old ones in new ways. Sending yourself (with your own set of experiences and thoughts) into a place where people think differently can spark a whole host of new ideas.
At the very least, you'll learn something about the world, and about yourself.
Travel helps you connect the dots between the way you think and the way other people think. That doesn't mean you have to go all the way around the world—changing cities and meeting some new folks will do. To think new thoughts, you have to wrestle yourself out of your familiar daily patterns.
I've heard of a trick where, in an effort to change routine, you can start brushing your teeth with your left hand (if you're a right-y, for example) or go through your morning routine backwards. I've never tried it myself, but it sounds like a good start.
What travel does, though, is it takes your whole life and turns it into brushing your teeth with your left hand. You're wrenched out of your comfort zone: what time you wake up, what you eat during the day, what you see and do and learn. Travel is a shock to the system, one that starts to make the whispers of ideas in your head grow into something more.