I think Barry Allen is physically incapable of not being friends with absolutely everyone, but he's closest to Hal & Ralph. The only Leaguer who rubs him the wrong way is Ollie, who he considers a loudmouthed rich blowhard.
Much like Ollie, Hal Jordan rubs almost everyone the wrong way, particularly Batman, whom Hal goes out of his way to annoy. However, I think there is a deep-well of mutual respect between the two. As Bendis has been having fun with, Hal desperately wants to be best buds with Superman, who is too damned Midwestern and polite to ever rebuff his advances. Hal has tried literally every possible way of flirting with Wonder Woman over the years to no avail, because Diana delights in pretending to not notice and completely ignoring him
Agreed on Hawkman, with the notable exceptions of Shayera & Ray Palmer, who is also a bit of a loner.
Ted, Booster & Scott are old buddies and still go out for beers regularly, as shown so well by King & Gerads recently.
I never understood Meltzer's idea that Aquaman & J'Onn are secret best buds. Aside from their brief time together as the only two JLA founders in JL Detroit, I don't see the connection there. Is there some story where these two bonded or something?
I don't think Dinah & Diana are particularly close. I think they both respect each other quite a bit, but Diana is too damned intimidating to a lot of women. They look at this perfect goddess and only see their own failings.
Ollie & Bruce get along well enough because they both recognize that, at heart, they are cut from the exact same cloth. They are both rich kids who've bought their way into Olympus to stand alongside the Gods. As result, I think Ollie is more competitive with Bruce because he recognizes that he's always going to be seen as a lesser version of Batman.
Zatanna is an outlier. She's closest to Barry, but she keeps her distance from most. She doesn't particularly like being on a team. She likes all the attention to be on her.
The various GLs share a much stronger bond these days, with Simon & Jessica being close. Jessica viewing Hal as a father figure who she both idolizes in an unhealthy manner while also rebelling against to show her own independence. Guy still hates Hal, but only because he's jealous of him. In his dreams, Guy Gardner wants to be as cool as Hal Jordan and never will be. Hal & Kyle have a big brother/little brother thing going on. John & Guy are very tight. John & Kyle less so. John & Hal's relationship is extremely complicated. I would love to see a deep dive on these two and how they both love and hate each other. Alan Scott privately disaproves of all of them and considers them all a bunch of reckless hotshots.
Jay Garrick loves everyone.