Free weight squats would do a lot for your core, legs, and back -- consider at least doing those in addition to your other stuff. When I work out, I prefer the larger compound movements for functional strength and efficacy over isolation exercises like curls.
If the gym has rowing machines (and they ought to if they spent 5 million squiggly things), I love those because they work darned near everything in your body and you can shift the emphasis as you go.
