1. Cincinnati Royal PF Maurice Stokes doesn't have his accident during a game in the late-50's, and he plays with Oscar Robertson in the 60's.
2. I would still have the Lakers move to LA, but I would have the Syracuse Nationals move to San Fran instead of the Phila. Warriors (which makes more sense to me). Then, I would rename them the San Francisco Sharks.
3. I would have the Royals win at least two titles that the Celtics won, if not more. Stokes and Robertson would have been a dynamic duo, and they also had Jack Twyman, Jerry Lucas, and Wayne Embry. That would have increased interest in the team, butterflying away their 1972 move to Kansas City.
4. I would have the Chicago Zephyr/Packer team stay put rather than going to Baltimore. Then, I would re-name them the Bulls in 1965.
NBA 1965-66:
Eastern Division: Boston Celtics, Cincinnati Royals, N.Y. Knicks, Philadelphia Warriors
Western Division: Chicago Bulls, Detroit Pistons, L.A. Lakers, San Francisco Sharks, St. Louis Hawks
1966-67: Since there are only nine teams instead of ten (no 76ers added in this timeline), the NBA only expands to Seattle (Supersonics). They beat out San Diego and Pittsburgh. The Sonics are put in the West, and the Pistons are moved to the East.
1967-68: The ABA begins play with eleven teams (Anaheim Amigos, Dallas Chapparals, Houston Mavericks, Indiana Pacers, Denver Rockets, Kentucky Colonels, Minnesota Muskies, New Orleans Buccaneers, New York Americans, Oakland Oaks, Pittsburgh Pipers). As a result, the NBA decides to expand again, and they put teams in Milwaukee and Phoenix that will start play the next season.
1968-69
Eastern Division: Boston Celtics, Chicago Bulls, Cincinnati Royals, Detroit Pistons, N.Y. Knicks, Philadelphia Warriors
Western Division: L.A. Lakers, Milwaukee Bucks, Phoenix Suns, San Francisco Sharks, Seattle Supersonics, St. Louis Hawks
Summer of 1969: The New York Nets (they were re-named that after their first year) were able to steal Kareem Abdul-Jabbar away from the Bucks and the ABA. Also, the Hawks move to Atlanta, and flip divisions with the Bulls.
1970-71: Cleveland and Portland enter the league (Buffalo misses out in this world). This is how the 14-team league looks now:
Eastern Division: Atlanta Hawks, Boston Celtics, Cincinnati Royals, Cleveland Cavaliers, Detroit Pistons, N.Y, Knicks, Philadelphia Warriors
Western Division: Chicago Bulls, L.A. Lakers, Milwaukee Bucks, Phoenix Suns, Portland Trail Blazers, San Francisco Sharks, Seattle Supersonics
Summer of 1972: After the dominance of Kareem and the Nets, the ABA and NBA decide to talk merger (the NBA wants Kareem and that team in their league). At the end of those talks, it was decided that the New York Nets, Indiana Pacers, and Kentucky Colonels will enter the NBA. However, since Kentucky is such a small market, the team decides to move to Kansas City as part of the merger agreement. They are re-named the Scouts (after a statue that is in Kansas City).
1972-73 NBA alignment (17 teams with four divisions):
Eastern Conference
Atlantic Division: Atlanta Hawks, Boston Celtics, NY Knicks, NY Nets, Phila. Warriors
Central Division: Cincinnati Royals, Cleveland Cavaliers, Detroit Pistons, Indiana Pacers
Western Conference
Midwest Division: Chicago Bulls, Kansas City Scouts, Milwaukee Bucks, Phoenix Suns
Pacific Division: L.A. Lakers, Portland Trail Blazers, SF Sharks, Seattle Sonics
After that, I don't think that I would add too many more teams (maybe five to seven at the most. I don't think the NBA should have more than 22-24). Also, I would probably wait until the late-80's before thinking about expansion because popularity declined in the 70's, and you want to take time to build that back.