In my own narrative in my head:
Rory has a boy named Rory
Logan dumped odette, proposed again to Rory who again turned him down as she knows he only proposed because she's pregnant (if he really loved her he'd have dumped odette as soon as they got back together) pays a good wack of maintenance and sees the child sporadically.
Stars hollow gazette, using the money and fame from the bestselling 'Gilmore girls' book is now online as well as print and giving real competition to Conde Nast and Huntzberger media Corp (which is royally pissing off Mitchum).
Jess is working at the gazette too. But also writing his own literary fiction.
Following a drunken night celebrating a rejected proposal of a buy out from Mitchum, Jess and Rory marry in Atlantic city, they awake to hungover realisation but following stilted awkward hungover discussions and because Jess is amazing with Rory Jr. They decide to stay married.
Emily and Jack get engaged but decide not to marry but just live together - lorelai's reaction is somewhat Emily like 
Paris and Doyle get an elevator and another baby, to Rory's and Doyle's surprise as a reaction to almost losing the baby, Paris decides that she will be a sahm - being Paris she embraces this completely and becomes a vocal advocate for attachment parenting, extended breastfeeding etc
Lane invents 'parent rock' hep alien becomes very successful with songs about the joys and challenges of parenting! Paris is a BIG fan!
Michel and husband adopt, Michel runs the new inn with spa with huge success initially, but then realises he wants a better work/life balance so hires a deputy manager to give him more time at home. Fatherhood was not initially easy but now he adores his children.
Sookie comes back to the dragonfly, that's really home and after Jacksons death in a tractor accident she needed to be home, so did the kids.
Patty gets a FABULOUS toyboy.
Taylor FINALLY comes out at Woodbury pride march.
Lorelai and Luke are stunned to find lorelai is pregnant - with twins - honeymoon babies! Lane is thrilled to be able to advise lorelai on mothering twins. Lorelai freaked a little at first but Luke was so thrilled and Emily so shocked she embraced the news, after Emily had brought her a mustard covered pretzel and said "you're doing this. You're a Gilmore".