Training Martial Arts Without Coaching is Not Recommended
I came to the same conclusion you did in this answer on Stack Exchange Fitness: skill development without a partner and without a knowledgeable instructor is very hard, slow, and prone to producing bad habits instead of ability, so you're better off becoming a beastly physical specimen instead. Your goal should be to become strong, powerful, mobile, and able to perform vigorous tasks without tiring. The question of how to do that is extremely broad and depends very much on your current physical abilities and attributes. Fitness.SE is a much better place to start that inquiry.
Attribute Development Prior to Martial Training
The short answer for "what should I do instead" is to develop the primary physical attributes for combat sports: strength, power, mobility, conditioning.
To do that, you'll first want to have an aerobic base, best developed by running, swimming, rowing, or biking over medium-long distances. That could mean getting a solid mile or 5k time, or rowing 2000 meters on a machine. At the same time you'll want to train basic calisthenics for strength, as prerequisites for barbell training: push-ups, pull-ups, dips, air squats, lunges.
You'll also make sure that you've got the necessary mobility for rigorous training, like an effortless third-world squat, overhead shoulder position, and being able to touch your toes. If you're not fit, I'd recommend the training program in Robb Wolf's book, The Paleo Solution (which is mostly about diet, but has a very respectable ramp-up program for physical training). Yoga is also a solid staple, and ideally should be practiced weekly throughout your training.
Once these basics are in place, the more important heavy resistance training can begin: loaded squats, deadlifts, bench and overhead presses, power cleans. Barbells are best for this task. To learn how to use a barbell properly, the book Starting Strength by Mark Rippetoe and Lon Kilgore is a great resource. At this stage of training your runs would become less frequent (once a week or every two weeks). Bodyweight calisthenics can be relegated to warm-up or accessory exercises at the end of a workout, or you can use bodyweight exercises as your upper-body resistance training: pull-ups, chin-ups, and dips are all productive and can be used with additional weight. Hindu push-ups and their advanced counterpart, handstand push-ups, are tough to load with additional weight but are extremely useful nonetheless.
Setting long-term goals like a double bodyweight deadlift or a bodyweight press are helpful in spurring progress as long as they don't cause you to overlook injuries or mobility problems.
Short, high intensity conditioning work such as kettlebell, dumbbell, or barbell complexes, sled drags and Prowler pushes, sprints and hill sprints would fit in a few times a week after you've developed a reasonable level of strength--more than five pull-ups, a squat loaded with your bodyweight for reps, a greater than bodyweight deadlift.
Eventually you'll want to prioritize developing power in addition to strength. Exercises would include snatches, jerks, push presses, broad jumps, height jumps, sprints, and increasing the priority of power cleans. Benchmarks such as a bodyweight clean-and-jerk or being able to jump up to sternum height are useful goals.
At that point I'd also consider gymnastics: bridges, work yourself up to a pistol (and then jumping or weighted pistols), front and back levers on rings or a bar, muscle-ups, and so on. These feats build on your strength base and develop other attributes like balance and coordination. They're also clearly impressive.
This training would take several months to several years, and would well prepare you for technique training and sparring once you have the chance.
