The following are some things you should not consider when choosing a dojang/instructor:

• Nationality or Gender. The race or gender of the instructor is completely unimportant. Do not assume a Korean Taekwondo instructor is better than any other instructor. Do not assume a male instructor is better than a female or vice versa. What matters is whether the instructor can instruct and inspire your to be the best you can be at Taekwondo
• Aesthetics of Dojang. You do not want to train in a dump but otherwise the appearance of the dojang is not that important.
•  Superfluous Stuff. A good dojang needs a clean, safe training area, punch/kick targets, punch/kick bags, maybe some mirrors, and maybe some mats. Do not be overly influenced by unrelated stuff, such exercise machines, weight room, hot tubs, tanning beds, etc. If you want to pay for all these extras, that is okay, but they are unnecessary.
• Uniforms. Do not be influenced by flashy uniforms. Be suspicious of dojangs that use uniforms that are too different from the norm. 
• Appearance of Instructor. A skilled Taekwondo fighter will probably be in excellent physical condition. A skilled Taekwondo instructor may be a physical wreck. When you are in need of medical attention, you do not care whether the doctor helping you is fat or not, you only care whether he or she can help you. Similar to good coaches in other sports, good Taekwondo instructors come in all sizes, shapes, and levels of fitness.
• Rank. There is no universal Taekwondo ranking system.  . Be suspicious of those claiming unusually high ranks. Each major Taekwondo organization has it own rank structure and is usually in a power struggle with the other organizations, so it is difficult to compare ranks between them. So do not base your decision on which dojang to attend on the rank of the instructor.