Outside, the Dojo.
There is something that has weighed on my mind for some time. Why has Martial Arts training moved inside? When did the idea of learning or training Martial Arts, as a general accepted practice, encompass the idea or concept that if someone wanted to learn Karate, Kung Fu, Jiu Jitsu, etc. they would be going into a well lit, air conditioned studio with mats from wall to wall? Don’t get me wrong, I fell into this same ideology as well. I don’t know the answer. However when I started researching (because I’m a nerd that way) I realized that the practice is very recent and almost exclusively isolated to Western Europe, and North America. (I would include Brazil, but it does not seem to follow that rule there, in my findings anyway.) For most of the world and all but recent history people have trained Martial Arts outside.
Training in the environment that is most similar to where you will need your skill set will definitely change your outlook on what you are learning or know.
MMA fighters practice in a cage, Boxers in a Boxing Ring, Soldiers do war games outside, Fireman practice putting out house fires by lighting a house on fire, and so on. Do yourself a favor and do the same thing. If you learn something in an indoor training facility, go home and practice outside with shoes on, in as many environments as possible. I could waste both of our time by explaining the multitudes of differences, but until you experience the difference you will not fully understand. It may save your life one day, and it will make you a better Martial Artist.