I feel like Lorelai have an almost other-world quality to her. My ESFP friend may be fun loving but she is also very responsible and practical. One is due to the fact that she grew up with an irresponsible mom and had to be the 'parent' since she was very young. Lorelai is more dreamy and her view on relationships seems rather idealistic to me. She just does not strike me as the down-to-earth, fun-loving ESFP. Her leaving her parents' house at such a young age strikes me as what an Idealist would to, to raise her kid independently and whimsically. And she have odd items in her house, was it a monkey lamp or something, that seems very ENFP, not ESFP. Aren't ESFPs more conventional with their tastes? I actually thought she was ENFJ as she is very good with convincing people to do her biding. And she is quite good with becoming an inn's manager which involves day-day mundane tasks.
If you think about Lorelai and Rory together, Rory took the 'voice of reason' but she may naturally not be that type. She seems INFP to me, but she have a very strong upbringing and was not emotionally traumatized as a child so she is good with dealing with her emotions and not as moody. She was raised to be confident, so she gives off an almost Rational Air, but she is very warm and considerate.
Logan as an ESTP would be her dual.
I have never been able to type Jess.
Dean struck me as ISFJ, with a knack for mechanics because his father is one.
Ah Paris, I love her, haha, quite an ENTJ that one.
Luke to me is ISTJ because he is always picking up after his sister, which is not INTJ at all. INTJs likes to force people to stand up on their own, no? Independence, competence and all. And that whole thing about his uncle who no on liked but he was good about following the funeral arrangements, out of a sense of duty. He is most def. a Guardian, though a rebellious one.