The VIC-II chip inside the C64 computer outputs a S-Video signal, which is mixed and modulated into the matal box that contains the UHF modulator circuit. Earlier models made composite video available on the A/V DIN connector. Later models also made separate componentes (luminance and chrominance) available as well.
For the sake of image quality, and as you say you want to use your C64 in a modern TV, it's better to forget about the UHF output.
Most modern TVs still have a composite video input (yellow, white and red RCA connectors at the back). If yours doesn't have it, it may have it in form of a TRRS output and you will need a cheap TRRS -> RCA converter. Others have it embbeded into the SCART connector. Others share the composite video connector with the YPbPr (video component) connector (actually using the Y connector (green) for both luminance and composite video). So, your first and more succesful option would be to get a composite video signal and audio signal from the C64 A/V DIN connector and feed with it your TV.
However, if you find your TV supports S-Video (normally, a 4 pole mini-DIN connector) and your C64 is a later model that outputs S-Video, then you can try it as well, for a slighly better video output.
So your first (and cheaper) options are first to find an A/V cable for your C64, such as this one:
Or this one, if you can confirm your TV supports S-Video input and your C64 can output it as well. Note that this cable can also be used with older C64 computers / TVs which supports only composite video.
If (and only if) your target monitor doesn't accept either composite video or S-Video, then you can try a converter box. This one I bought some time ago can accept both composite and S-Video inputs.
This is the device, once unboxed and connected to a composite video source and to a TFT VGA display:
This is how I see a C64 computer in my TFT monitor. Its monitor OSD shows me which VGA output resolution I'm using. Although it is using the composite output from the C64, I think it gives a very decent image.
There are several resolutions and refresh rates availables:
The converter brings its own OSD menu, from which we can adjust many parameters. This is just one of the sections:
This particular VGA converter box allows a VGA source too, so you can share your mnitor with your PC and your C64 without the tedious connector unpluging and pluging. Just pressing a button. You can even have a PIP (picture in picture) output.
Of course, you can go for a composite-to-HDMI, or S-Video-to-HDMI converter box, if you are willing to use a monitor/TV without VGA input. Amazon sells them with different prices and options. These HDMI converters usually convert the audio signal also, so you have a true HDMI audio/video signal. I have one such converter, but I haven't tried it yet with a C64.