I kind of had to jump around to different places as a kid so this might be long. I was 9 or 10 when the first MK was new in arcades so I'm having fun thinking back to that time.
The first place was the arcade called the Gold Mine in the Sandusky Mall. My parents would go to the mall every two weeks or so and I was allowed to go off on my own mostly. I'd play MK there but a lot of my MK experience was at home on the Sega Genesis. I do vividly remember walking into the arcade one day to play MK and noticing a crowd of people around that area. When I got closer I saw that everyone was gathered around MKII. My mind was completely blown. It was a complete surprise that it even existed. I watched people play for a while and I remember seeing a guy do Johnny Cage's Friendship and I couldn't believe how awesome the game was. I don't even think I got a chance to play that time because there was such a crowd (all people older than me) around the game. I do remember going to the book store in the mall and getting some gaming magazine with an article about it and the moves/fatalities. I couldn't get to the mall often enough to play MKII. My parents wouldn't take me just to play since the mall was about 30 minutes away. Then at one point the arcade in the mall was closed for remodeling. It had been a very 80's style arcade with no real lighting other than the games themselves. The remodel seemed to take forever, but luckily a movie theater in the same town as the mall had an MKII cabinet by that time. My parents would drop me off while they saw a movie and I'd play the whole time. Still, I only got to play once a week at most.
At some point a video store about 10 minutes away got an MKII game. So I got to go there more often. I've never been a pro tournament level player or anything, but I could always beat most people who randomly came up to play so it was always fun to surprise older kids and adults who thought I was just a kid messing around. I do remember one instance (at the movie theater I mentioned before) when these 2 brothers came into the arcade. One was older than me and one younger. The older one came up and put some quarters in to play me, fully expecting to destroy me. I even remember I was Sub-Zero, not sure who he was. He was getting mad that I was using block when he attacked. So mad that his brother kept hitting my hand off the block button and when I pushed him back a little they sort of backed me into the side of the arcade machine as if they were going to fight me in real life for beating them in the game. They ended up just sort of trying to act intimidating then leaving.
So anyway, by the time Mortal Kombat 3 came out, the arcade in the mall had been remodeled. It was now a brightly lit space with glass windows so you could see in from the mall itself. I was disappointed because half the time there was glare on the screens. I'd play MK3 there, and at a local comic book shop. Once I walked into the comic shop and this kid was playing MK3, I think as Smoke. He had a few people watching him and he was killing the computer opponent, and being a real show off about it. I remember he actually said after one match, "See how I always beat them with so much time left on the clock". Having watched a few matches I felt like I'd have a chance against him. It turns out I destroyed him. I've never been much of a trash-talker, but I was sure to point out to his buddies how I beat him with even more time left on the clock. Again, I'm not a great player, but these little stories still stand out in my mind when I think back. The other MK3 machine I frequented was in the little entrance way of a department store called Harts.
When UMK3 came out it seemed like nowhere around me got the upgrade. I found one eventually at a sports card store. It was kind of far away and I never really got to play it much. Then there was MK4, which I played at the little arcade that was in the newly built Super K-Mart in town. By that point I was playing console games at home mostly, but MK always brought me back to the arcade until 4 was available at home.
Well there you have it. A not so brief history of where I played MK. Ever since true arcades pretty much died off, it's always fun to come across the occasional MK game in random places.