I've struggled with knee pain for quite a long time myself, so I can emphasize with you when it comes to this issue. There are mainly two things that have helped me when it comes to remedying knee pain while biking.
The first is, as you mentioned, to adjust the seat height. Depending on the height of your seat, the angle at which your legs have to pedal changes the amount of pressure you put on your knees. Experiment with different heights to see what works for you.
Another crucial element is to buy a multi-speed bike if you don't own one already. The effort it takes to pedal on a single-speed bike can sometimes be too much for some people, so being able to adjust the gear depending on the incline of the road can make things a lot easier for your knees