You can buy a C64 DIN video cable that will put out s-video, composite video, and audio. From there, you will need a converter box to go from s-video or composite to HDMI. There are cheap and crappy converters and there are better expensive ones but the C64's video output is never going to look amazing anyway.

Alternatively, you can skip the converter box and buy an old TV with s-video input instead.

Thrift stores and garage sales are good places to find tvs with composite inputs cheap. That’s what I would do.

The C64 can output composite video natively (with the yellow, red, white cables). You could buy or build yourself such a cable and then use an composite to hdmi converter box to use your modern monitor. Although I do not know if cheap ones will work with the signal, you have to do some more research on that.

I think you pretty much understand the issue here. The C64 has composite video output through a DIN-to-RCA adapter and analog television output through an RF converter. There is no option for digital outputs to modern monitors since they did not exist when the C64 was manufactured and they use a completely different set of signals.

Your options are pretty much to:

1. Find an analog monitor or TV with RCA inputs and buy or build an adapter cable,
2. Find an analog color TV and use the RF adapter (which will give you far worse display quality), or
3. Try the converter box, which I hear is a hit-or-miss option.

This is the fun of going retro, no?

This discussion on lemon64 might be of relevance. Maybe using the rf output might work, but they mentioned that there could be some quality issues.

One extra path might be a home theater type amplifier. Some have composite and svideo inputs and can upscale to HDMI resolutions. Often cheap and common second hand and you also get an amp. Takes some reading and hunting, but might be easier to find and use than a more focused solution.

Easiest: Find an old 4:3 flatscreen vga monitor that also supports composite. There’s a fair number of them out there. Best: retrotink but that’s going to probably cost more than the c64.