I would say the St. Louis Cardinals, the only team to appear in the World Series 3 times in the 1980's,
winning it in 1982.

Perusing All-Experts.com gives me this:

"Here's a list of the four teams with the most wins in the 1980s, along with their winning percentage:

New York Yankees 854 .547
Boston Red Sox 841 .525
Detroit Tigers 839 .536
LA Dodgers 825 .527
St Louis Cards 825 .529"

http://www.allexperts.com/user.cgi

So in terms of winning percentage and number of wins, the New York Yankees were the best team of the 1980s. They made it to the playoffs only twice in the 1980s however, losing the ALCS in 1980 and the World Series in 1981.

In terms of playoff wins, the St. Louis Cardinals and Los Angeles Dodgers were the best teams. They had a total of 21 playoff wins in the 1980s (as compared to only eight by the Yankees). In fact, only six teams had over 10 playoff wins in the 1980s:

The Dodgers and Cardinals (21 each), the Athletics (16), the Royals and Phillies (13 each) and the Mets (11).

In terms of World Series appearances, the Cardinals made the most, three. However, they won only won and lost two. The Dodgers made two World Series appearances, winning both.

I'd have to say that the best overall team of the 1980s is a toss up between the St. Louis Cardinals and Los Angeles Dodgers, with the Yankees being a runner up.