Yes there is, but you are going to get frustrated. It's called VMK Central and it's about halfway down on the right on Main Street. There are maybe four terminals, and I think they are older than I am (I'm ancient, trust me). The keyboards are atrocious to use and the screens terrible.
However, if you create a new character while at a park, you receive special clothing, special black ears, I think an extra room, and a "Born in Park" badge (not a pin, a badge).
The last two times I was at a park, given the horrible computers, I did not create a new character. I sent a few in game messages to friends just so they had a message from someone at a park.
You will not be sitting there playing VMK. no chairs! Besides, getting out and enjoying the parks is what you want to be doing there anyway! Do the quests, get your quest cards, maybe create a character for the novel stuff, then get out! Go play for real!