I'm not sure about Asian teams, but The Clevelander on South Beach at 1020 Ocean Drive is a fun place. During all games you get $3.50 Bud Light Drafts and the $11 Hot English Breakfast special. Also, Fritz and Franz Bierhaus is ideal for matches against Germany, Austria and Switzerland. That's located at 60 Merrick Way in Coral Gables. The French like to go to Le Bouchon du Grove at 3430 Main Hwy. in Coconut Grove. When all else fails, go to John Martin's at 253 Miracle Mile in Coral Gables. They have plenty of TV's and offer free continental breakfast during morning games.
Agree with Rosemary The Playwright (Washington and 13th St in Miami Beach) is a favorite, full of european 'connoiseurs'. Furthermore, once the match is over, is a short walk (2 blocks) to the Beach, in my opinion, better than the Clevelander (if you are for 'football').
For the rest agree with Dina, Fritz and Franz is also full of europeans and pretty fun.