Actually, I'll go into more detail.
If your primary goal is using the gym to better your taekwondo-based athleticism, you are looking at pretty simple stuff.
First, let's think about what you want to get good at -
-upper body spinning
-Jumping
-leg speed
-Foot agility
-kick power
-punching power
-flexibility/joint mobility
First of all, you don't even need a gym to properly build these areas. They can all be trained purely with bodyweight exercises. However, since you too have the luxury of a gym membership, I'll suggest some great taekwondo exercises-
ROUND KICK POWER
-Heavy bag
-Sprints
-Hip flexor machines
-Cable hip flex
-Tuck jump
-Depth jump
-Calf jump
-Leg extension machine
-SQUATS
-Oblique exercises: I recommend cable woodchoppers highly
SIDE KICK/BACK KICK POWER
-Heavy bag
-SQUATS SQUATS SQUATS SQUATS
-MORE SQUATS
-Any glute machines
-Ab exercises
SPINNING KICK/HOOK KICK POWER
-Heavy bag
-Ab exercises
-Oblique exercises
-OBLIQUE exercises
-Oblique exercises
PUNCHING POWER
-Heavy bag
-Bench press
-Push up
-Dip
-Shoulder press
-OBLIQUE EXERCISES
-Possibly serratus exercises
-Flies
-Cable punch
-Dumbell punch
CHOP/BACKHAND POWER
-Rear felt fly
-W raise
-Chin up
-Row
-Lat pulldown
JUMPING
-NO BOX JUMPING
-Depth jump
-Vertical jump
-Lateral jump
-Long jump
-SQUATS
-Bench SQUATS
-Jump SQUATS
-Lateral raise
-Front raise
-Backflip
-Calf raise
FLEXIBILITY/JOINT MOBILITY
-Umm... Just stretch.
Just figure out what muscles you need strong, and work them. Purely for strength, the ideal way is to keep reps to 5-6 very difficult reps/heavy weights. For mass, just rep until the body part is completely exhausted.
