I quite like some of the speculation I've heard around FO4, alot of it has said it will take place in Boston and will focus around the Commonwealth. Think I remember something about the main quest possibly being about the fight between androids and the commonwealth.

Whatever the case, I hope they go for the kind of atmosphere FO3 had over FNV. I found FNV to be far too...unapocalyptic feeling, there was no where that I thought "I'd rather shit the bed than go in that building" or anything that made me feel sad or unhappy.

I also hope they don't make it like Skyrims quests. I found Skyrims quests were all very hollow and kinda like the quests came to you (Like you kind of discover them as you're doing other quests), unlike FO3 where you had to go out of your way to find them. Also too many quests that decided the fate of the land or the world or the ENTIRE UNIVERSE. (Main quest, Wolf queen, Dawnguard off the top of my head)

I'd love to see a story that starts you off as a soldier returning from Alaska or Saigon or wherever the US Army was prior to the world being nuked only to be met with the sight of your hometown in (more or less) a smoldering heap. You then are faced with the moral dilemma - do you do what you can to help whatever survivors are left or do you take what you can from them to ensure your own survival.

It'd be cool, too, if (as @happysheep stated), your actions didn't decide the fate of the "ENTIRE UNIVERSE" but rather a small group of orphaned children trapped in a school or a radiation-sick family. On top of this, maybe you'd be able to watch factions, both inherently good or bad, form. Possibly even return to a group of people who were once dead-set on helping others to find they've devolved into cannibals or raiders in order to survive.

I'd like some sort of chapter system...

Like complete something in the main quest-line and Ron Pearlman will narrate a little about what's going on.

Also, multiple start options. Did you come from a vault? Were you a raider? A caravan guard!?
The choice is yours!

Hmm, I actually thought that the theme around that Fallout 4 hoax was really interesting. Maybe sounds stupid and Beth would probably never do it, but I kinda liked it.

Something involving the commonwealth... I could definately see a situation where the person who's in charge of the commonwealth is using the technology there to rule over the Boston inhabitants. Maybe the BOS is trying to overthrow the commonwealth.. Some BOS members want to overthrow the Commonwealth simply for the technology loot, and other members want to legitimately free the Boston citizens from an oppressive government.. Many interesting avenues this game could take.