The Modoc quest springs to mind and the gecko quest (I hate first citizen Lynette).One of the most poignant moments in Fallout 2 IMO is the
Spoiler Bit with Frank Horrigan attacking gruthar and Vault 13
but it does involve the enclave.
As styles said Fonv sets a good example for tone (and just about everything else IMO).It has a heterogeneous blend of wacky light hearted moments (fisto, psychic boy, talent pool quest etc and then fonv deals with cannibalism, slavery, corruption, the journals of a mans eventual suicide and Lilly's mental issues (quite sad if you think about it )etc.
But Fallout isn't about the day to day gloom and doom of survival in a post-apocalyptic world like the walking dead is for example, there is going to be hardship obviously but they aren't the focus of the narrative but rather long term progression is via rebuilding society. So I don't want to see this "Just the whole horror and constant danger of not only the creatures in the wasteland but the people".
Also I've never really noticed the overwhelming juvenile humor in Fallout 2 to the extent that it tarnishes the game
Sure there's a porm studio, a scorpion you can compete against, a talking spore plant, hakunin, 4th wall breaking random encounters, hubologists and so on but there's still lots of maturer/darker content as well.Though having said that I also feel Fallout 2 is a step down from Fallout 1.