I'd suggest getting a kettlebell and paying for a couple of kettlebell classes. You need to learn proper form and once you've got that down, you can either do it at home or take it with you when you travel (I've traveled with a 25 pound keettlebell on my carry-on a couple of times with nothing but "oh... that's nice!" from TSA).

Pair that with a jump rope and you're all set for home/travel and cardio/strength.