In popularizing the game, I play tennis because my mom had a crush on Borg when she was a teenager and started playing tennis because of him. She's not from the US, though. Mac and Connors allegedly reinvigorated tennis in the US (according to my dad, at least, I wasn't alive). It's too difficult for me to say much about the Pro-era dudes because that's so far removed from anything I know about.
As far as influential otherwise, I feel that it has to be Arthur Ashe.
Ashe protested South Africa's Apartheid, raised awareness about heart disease and AIDS, and spearheaded the ATP.
Althea Gibson, Billie Jean King, perhaps Gottfried Von Cramm, and maybe Martina (I dunno how big of a deal her defection from the Iron Curtain to the US was).