Bill Bradley and Princeton get another chance to prove that Ivy League basketball isn't all that bad when the talent-packed NCAA tournament moves into its second round tonight.

Earlier this week Bradley poured in 34 points as the Tigers drew away to an 26-60 win over V.M.I. in the tournament's first round. Since V.M.I. had upset nationally ranked Davidson to get into the NCAA's, Tiger coach Bill von Breda Kolg was unusually happy.

The Princeton conch's jubilation might reach new heights tonight, since the Tigers have a good chance to win and reach the tournament quarter-finals. They face a University of Connecticut team that came into the tournament with a so-on 15-19 record and only the Yankee Conference Championship to its credit. Ucom dropped a game to Yale, its only Ivy League foe, earlier in the season.

Whoever wins tonight isn't going very much farther. In Saturday's quarter-finals, the winner has to face either Atlantic Coast Conference Champion Duke (23-4), or Villanova (22-2), the country's fifth-ranked team and top defensive squad. Those two meet tonight at Raleigh in one of the two top games on the NCAA card.

The other contest takes place in Minneapolis, where defending champion Loyola of Chicago (21-5) meets Big Ten powerhouse Michigan (20-4). It's a tough draw for both teams and a lucky one for Kentucky (21-4), one of the top pre-tournament favorites. The Wildcats meet the tired winner of the Loyola-Michigan game tomorrow if they can dispose of Ohio University (20-5)--a much easier task--tonight.