From all the background info I've read, and behind the scenes footage that's escaped, the TNG cast does seem the most closely knit. This might be because in 1987, no one really knew if a new Star Trek series with new characters would work. Especially as it wasn't a network show, and syndicating a brand new dramatic series hadn't been done in decades. They were all either climbing the mountain or falling off the cliff together. The only familiar names to American television audiences at the time were LeVar Burton (Roots in 1977) and Wil Wheaton (who'd had a hit film the year before with Stand by Me).
This stepping into the unknown likely helped the cast to bond quickly.