Lots of really great responses in this thread. Here are my .02.
1) I agree with Peter MT is an awesome art but I get no meditative benefit from it. The main reason I don't train MT more often is that I hate getting punched in the face. Pretty much that is a standard part of the deal with MT. I have also done Kendo and when you are putting on your armor at least you are meditating (or supposed to be) at that moment before the chaos starts.
2) I also agree with Ben. For me it is a stillness in my mind that settles in right before I grapple with someone. I can be laughing and joking around but when they say grapple I just flip the switch and everything changes. I watch video of myself grappling and see myself doing things I don't remember even thinking about.
3) Peter also nailed it with check out the school and the vibe. If you fit in with them and feel comfortable the rest will fall into place.
For what it is worth I do MMA two days a week along with No-Gi BJJ and BJJ 1 to 2 days a week schedule permitting. This way I am at least working a little on the stand up aspects of the game. In the end if you like the school and you practice your zazen on the side I think you will be amazed at the results.
One last thought. I am sure you are in a different place then I was mentally at the time. When I trained Akido we used to end our sessions with some meditation. Most of the time I meditated so well I would just fall asleep. Not exactly what I was after