Ah, I see - originally I thought you were referring to an erg machine (cardio). If you need strength alternatives to rowing, here are a few off the top of my head:
Upper back:
Lat pulldown - can be on a dedicated machine or on a cable machine with a wide handle attachment
Pull-ups - using a somewhat wide, overhand grip (like in the pics at the link) will work your upper back hard. If you're unable to do a pull-up, you can use an assistance machine (if the gym has one) or modify by hopping up to the top position, holding, then slowly lowering down. Other grips (hammer grip, chin-up) will work arms more than back but are still great exercise.
Mid-back:
Cable machine row - just need a cable machine with a seat and the appropriate handle to attach. Great back workout.
Bent-over barbell row - Can use a squat rack or a bench with a barbell.
Dumbbell row - just need a dumbbell and a bench.
That's my go-to rotation for back work.
