I think staying in hostels would be a great way to travel on a budget. This will not only be easy on your pocket, you'll be able to visit more cities in a country at a time. Plus, you'll get to interact with people from different ethnicity, which is an experience in its own way.
Start with South East Asia. Thailand Vietnam Cambodia - you can do all on a shoestring budget. Well worth the money!
Right now my suggestion would be to stay home and stay Safe
Vietnam is cheap and very beautiful
And even Bali if you spend wisely
You should Check out about Crowdsurfing it would save you a lot of money for you (Not recommended for large groups). It's a world travelers community. You can go to any country there will be kind people who would help out tourists.
There are many countries in central and southern America-Paraguay,Ecuador ,Nicaragua ,parts of Europe like czech , slovenia hungary and African countries like Malawi, Morocco with great wildlife and views which are not that expensive