I have a friend who's been traveling for the past two years and travels only by finding places where she can exchange her time, energy, and talent for a place to live, considerably cutting down on all of her travel expenses and, more importantly, teaching her a lot about life and herself while she's at it. She's worked on farms in New Zealand, studied permaculture in India, done remote consulting work in Australia, run a small hostel in Bali, the list goes on!
She's one of many people finding immersive, local travel experiences by using tools like Workaway, for example, a platform to find these kinds of exchanges. This is great if you want to independently organize your volunteer work overseas. If you'd like help finding the right opportunity and have in-country support, you can work with reputable volunteer organizations to help you find the right experience, as well. Intensive language study is also a great way to dig into one community, participate, learn, and grow from your travel experience.
With all of these options, you have the added benefit of walking away with new skills and solid experience you can add to your resume or speak about in an interview in the future.