Mullvad.net (a VPN provider) gives 3 hour accounts for free. You solve a captcha and they give you an account id to use to connect to their servers. If you want to keep using that account id for more than 3 hours you have to add money to that account. You can pay them in cash (they're in Sweden though) or Bitcoin, credit card, etc. They don't even ask you for your email and they claim to not keep logs that would allow to match an IP and a time stamp to a user [1].
One more thought - connecting via a temporary Mullvad account from a public or obscured entry point (perhaps during an international trip or at a McDonalds) would probably be the most straightforward method. The worst you're giving away is that entry point (to Sweden's loggers), but the DO/VPS fraud detection is less likely to fire if you're going through Mullvad.
To be clear, my own goal in all of this is primarily to get through residential ISP snooping -- I don't trust them not to sell my personal info. Staying out of the state dragnets is also a plus (I don't like the idea of snoops in a building somewhere reading my personal emails; same reason I close the living room curtains in the evening).
Yes, one can "anonymously" use WiFi APs. But it's hard to get close enough without becoming observable. And more and more, without being videoed. I've played with a Ubiquiti radio and parabolic antenna, and can hit APs at several km. But then, the dish is pretty big, so you need a large window. And unsecured APs have become harder to find.
It’s a lot easier to escape surveillance in the suburbs and rural areas. That being said, the ratio of McDonalds franchise density to population density goes higher the further out you go (at least in the US).
Note - Sweden is one of the “14 eyes”, so your browsing session (origin and destination IP, date/time) very well may be logged by their backbone, if not by Mullvad itself.
[1] https://torrentfreak.com/vpn-services-anonymous-review-2017-...