I noticed occasionally on some of the Sheiko cycles leg press pops up. i dont have a leg press where i train.
I know exercises like front squats and high bar squats are good quad exercises, but i'm thinking putting the leg press in was designed to allow you to keep working the legs whilst getting away from spinal loading, so choosing exercises with more direct spinal loading is probably not best.
We have a trap bar at my gym, so how about trap bar deadlifts as an alternative to the leg press? I've done them before and they really smash the legs without knackering your back out. They are more like a squat than a deadlift, but the bars not on your back.
I can see that as an alternative. Also, what about belt squats? If you have access to a low pulley, you can attach the cable to your belt and use some blocks if you need to add depth. Maybe dumbbell lunges or split squats with the back foot on a block or front foot elevated is another option. Also, if you are strong enough to do them, I am a big fan of one-leg squats, I usually use the support to balance myself (but not pull to cheat) and do full squats with one leg, you won't be using weight if you are doing them right. Just a few thoughts off the top of my head.