Here's an article that was in this month's Men's Health that talks about using portable resistance bands for use when traveling. I typically use the hotel gym but this could be a nice alternative.

Push ups are good for the upper back (lat) muscles.

Ab work should strengthen your lower back (actually a strong stomach will prevent lower back problems). I hate sit ups. I do crunches and leg lifts (lie on my back with legs out straight and lift my legs in the air 50-100 times. I do "sit backs", where I start in the position you normally end a sit up in and go back 1/3, hold it for 5 - 10 seconds, go back more and hold it again, and then go back until my back is almost touching the goround and hold it again. I do those 3 exercises in a row 3 times and also mix in some side twists with no rest between sets. Planks seem good, too, but I don't do them.

To work your calves, get on your tippee-toes. Just going from flat footed position to tippee-toes several times will work your calves. It's even better if you have some weight resting on your shoulders as you do this.

Using a chair and bed to do makeshift dips will work your tri's. Feet on the bed, hands on the chair and nothing under your butt. Dip down and then back up several times.

I don't do biceps work. That's a beach muscle. Big strong arms come from good triceps.

Same here. Whether or not to pack my running shoes is a big internal debate of mine on nearly each trip (unless I have to check a bag, in which it's a no brainer).