There are a lot of exercises you can do using the cable machine at the gym. Go to YouTube and search for arms and cable, or try stumpuous . com Just be sure that not just doing exercises for one muscle, like the bicep, and ignore the others.
Push ups and pull ups are great though. I do them modified/assisted and still get a great arm workout. I started by doing pushups against the wall, then moved down to a windowsill, and then a bench (which is where I am now). You can use a staircase in a similar fashion. I use the assisted pullup machine at the gym to do both pullups/chinups and tricep dips. I'm able to use less and less weight to assist me. Someday I'll do an unassisted pull up!