Use $J if you can, I try to use nothing but $J when there, even make sure to go home with some so I have it for the next visit. You'll also save a bit of money using $J than using USD and letting the businesses set the exchange rate.

As far as how much to bring... I'd think about how many you would normally expect to drink, then add enough to have a few more, just in case. I'd also bring a couple bucks for food as well, all that drinking with no food is a bad combination. We also tip Lenbert at least $2000J between the two of us.