I have the same issue, and it's finally starting to even out.
I agree with Skittl321 on the bilateral exercises. Just make sure you are not favoring your stronger leg when doing them. You should start to feel it in your weaker leg before you ever feel it in the stronger leg. When I started, my weaker leg would give out before I ever even felt it in my stronger leg.
If you do single leg exercises, you should still do both legs, but always start with the weaker leg. Make sure you only do the same amount with the same weight that you did on the weaker side. For example, you can do 10 lunges with 10 lb weights on your weaker side, only do 10 lunges with 10 lb weights on your stronger side even though you could probably do more. Since many leg exercises work several different muscles, this will also help balance out muscle imbalances in your stronger leg. Plus, it will be easier to tell when your weaker leg starts to catch up with your stronger leg
I do exercises like squats, step ups, and lunges. I guess the "easy on the knees" exercises depend on the reason for the bad knees too. My bad knees are mostly due to muscle imbalances so these exercises are good for me even though they may hurt. I just couldn't bend as much when I first started. It was the up/down motion that hurt the most, so I would often just bend into a squat or lunge position and hold it for a certain count. My knees have strengthened considerably since and I can do normal squats and lunges without pain.