What are some activities which are free or inexpensive that I can do to entertain myself / keep good mental health while searching for a better paid job?

Volunteering is a great idea, will also help you network work wise while looking for a job.

Teach yourself an instrument. I suggest piano because it’s super accessible. A keyboard can be had fairly cheap off Craigslist.

Bodyweight fitness maybe?

Attend free meetups of people in your career field (or the career you want). There's usually free food/beer, you learn things useful for your career, and you get to network with people and possibly get referrals for jobs.

Great way of learning an area is going for a walk and filling in questions for street complete, it's an app which let's you improve open street map. The data isn used in loads of places especially cycling apps where things like road surface are useful.

Sounds boring but it's actually really interesting

Cycling. You can get decent bikes second hand for pretty cheap. There's no better way to get to know an area than by cycling. Provided, of course, there are reasonably safe roads and cycling paths available.

Stretching. Good for flexibility, mobility, and you can combine it with meditation for an added mental health benefit.

I do some research online and watch a few videos for ideas.

Reading, stretching, hiking or just plain walking around the neighborhood or local parks, learning to cook and plan healthy meals…. These are all inexpensive and there is an abundance of free information available online. All of them encourage a healthy lifestyle, which will contribute to to good mental health.

Disc golf. Low bar to entry, many free courses.

Martial arts are also a great outlet. Many have forms practice on their school sites.

Pre-COVID I used to find software dev meetups. I found this patent law firm that did Haskell meetups once a month with beer and pizza. I guess they wrote custom software to analyze patents as I was surprised this was coming out of a law firm. Learned a lot and job openings were discussed by various members from other companies.

There's an app called GeoCache which is a fun way to learn a new area. People hide caches all around your city. The app shows you their location and you go find them, leave whatever you want inside (usually you just sign the log book), and then put it back. It's a pretty neat little scavenger hunt when you're in a new area.

If you're interested in meeting new people, look for a board gaming store. They're not common everywhere, but around here there are a few and they host public game nights. I met a few people on D&D night.

Idk if you have any interest in hunting, but the state hunting license class is pretty neat, teaches you a lot about wildlife conservation, and gives you an opportunity to meet and interact with local outdoorsmen.

The Fraternal Order of the Eagles has clubs all across the country, and they have awesome club houses. They're usually like a private restaurant or bar, often have game rooms, and host things like private poker tournaments. It's open to both men and women, despite the old-school name. There's some racism in their past, but that's all ancient history now. They're a really open group, at least here they are.

Last but not least, introduce yourself to your neighbors. If any of them are cool, invite them over for a BBQ or something. Or go out with them to do something fun, like hiking, biking, climbing , or shooting. The closest friends I've made since moving across the country have all been my neighbors.

Edit: adopt a dog! Dogs will keep you active, give you companionship, and increase your chances of meeting a human. There was a recent study that showed people walking dogs are way more likely to meet people while out than people by themselves, especially if the person is a male. Plus, they're just awesome. There are tons of benefits to owning a dog, including being happier, and living longer.

I make money off survey apps in my free time. I know you're looking for activities outside of the Internet, but while it's a grind, I've made 5K off survey apps over a couple of years, and haven't paid for anything on Amazon in three years. I am happy to tell you all about it. I imagine the money would be welcome.

Depending on your interests, chess may appeal. There's generally plenty of clubs around, and you have the social aspect of an activity with the learning curve of a hobby. Lots of clubs organise on Facebook. If you want to play rated games there's generally a fee (to pay national dues), but if you're happy just playing internally it's usually free.

Feel free to ask if you've any questions about how it works/is set up near me.

I have another suggestion; I am trying to teach myself how to make PowerPoint templates. Apparently selling them is lucrative. Maybe learning a skill is up your alley?

I get on Google maps and start looking for places to explore. No idea what it's like in your area, but I've found all kinds of neat places hardly anyone knows about, all within an easy hike.

You can start to create a music with some free programms. For example, you can download Reaper (trial version is working without any limits) plus some free plugins like Vital and you can find some free samples for drums and fx for it. For presets for Vital you can use site Presetshare. For publishing for free you can use soundcloud and bandcamp. But do it for yourself (not for popularity) and you will have a lot of fun