What exercises exist for increasing your strength in order to increase the amount of draw weight you can pull back on your bow? I was told just push-ups but, is there anything more that can be done?
From my archery days, you're primarily looking at upper arm and shoulder. Push-ups can help with that, but are pretty hard on your joints.
I'd be careful to intersperse these with actual draws as well, and to draw with both arms so that you don't end up off balanced. I use free weights, but I've always been leery of highly tailored workouts because unless you know exactly what you're doing you can isolate out important supporting groups.
I don't know how much push-ups will help, since they're working the muscles in a different direction. I started indoor rock-climbing this year at a place with some pretty healthy overhangs, and those work the back muscles in pretty much the same way as drawing my bow. It feels to me like it's made quite a difference.
Also, what's your draw weight and what are you trying to hunt? I'm just trying to understanding what's driving you to want to increase it, or figure out if it's even necessary.