A great hobby that doesn't require one penny (other than a good pair of shoes) is walking. I go on a walk every day and try to take a different route every time just to mix things up.
Some hobbies I enjoy indoors are jigsaw puzzles, crossword puzzles, and trying out a minimum of one new recipe a week. All three are affordable (although I sometimes find myself splurging on a really fun looking meal).
I'm not terribly good with my hands, so I've never gotten into woodwork, painting, or pottery, but I have friends who do and they swear by them. It's also fun because I'll barter some of our beef or lamb for a cutting board, serving platter, etc. It's a win-win for everyone.