Frankly I do not care where Fallout 4 takes place. As long as it is in the good old USA.
Chicago New York City and New York State would be something I'd like to see.
If we return to the West coast possibly San Fransisco or just the state of California together with parts of Nevada (salt desert, Area 51 Sin City
) and Arizona. (Phoenix...)
One of the things I would love to see is a bigger map. Because of the wasteland and lack of vegetation the feel of a big world is not present. Unlike for instance, oblivion, there are no forests to block your view. If you get in an Urban setting such as DC, skip the tunnel exploration (it can still be implemented as optional, because it was kinda cool to explore it, just not all the time. A a guy that hates fast travel for immersion purposes, I was forced to get in and out of the tunnels all the time) but allow the player to actually climb debris. Maybe a grapplinghook is a great idea, it gives a complete new feel to the city exploring.
It also creates a lot of possibilities. Instead of clearing out a building guns blazing, you can get to a higher building and snipe most of the inhabitants (or just shoot a Mini-nuke trough said window) The immersion and feeling that you are actually surviving out there gets a great boost, because everything you can do, the AI can also do
Another thing I would love to see is a feeling that time actually passes by. For instance, Big Town. I teach those kiddo's to defend themselves and they killed the Super Mutant threat, and are able to fight of the slavers. Wouldn't that make the town grow? Have some new kids running around from time to time? seeing them actually age? Turn that piece of [censored] hole to a prosperous town, that get acces from the traders and can eventually grow to become a hub like Megaton. The Big Townspeople could get materials from the destroyed villages surrounding it, using the materials to build more, or even better houses. They could even "Annex" germantown.
The noticable effect of your actions is minimal wich kind of svcks. Another example is freeing the slaves. You get them to Lincoln memorial and nothing happens. Nice beacon of hope for all slaves they managed to build in 10 years... It's still the same crappy place as it was before. You can (hypothetically) play the game for years (ingame and in Real life) but everything stays the same. You'd expect that after project purity with clean OPEN water available, vegetation would eventually return to the wasteland. (and don't give me the "It's only the tidal basin new player" treatment. Over time, a very long time, eventually the waters around the tidal basin would become free of radiation as well.) but it doesn't. I know there are mods that fix this, so it can be done!
Also a vault with people still living in it would be cool. Maybe there could be a random encounter of a exploration party of said vault that gets attacked by raiders. After helping them they take you to their vault, and from there on you can use it as a place to stay or barter whenever you want. (or even take over and become the overseer, having the people in it as your personal army of slaves)
Last, I would really love the standard stuff: More and deeper dialog and (saying this since Oblivion) Be sure that the new enginge gets some better facial features (frowning, twitches etc) You can hear the emotion in the voice, however the emotion you see does not match the expression you see. Have your NPC be able to frown is one of the first things to do. A lot of expressions make use of the stance of the eyebrows and forehead and the position of the mouths. it adds a lot!
Also, Longer main quest. I can complete the main quest (using fast travel) in under three hours. That's short. too short. The fast travel function is a curse, if you want to implement it have something like the Silt Strider in Morrowind. Fixed locations, so still need to explore a lot. Don't be afraid to have a main quest that's longer than 10 hours. (Got my hopes up for new vegas, Bioware have excellent and long main quests) Longer main quest doesn't mean fewer sales. Bioware did it with Knights of the Old Republic and that game sold very well.
Don't get me wrong. I LOVE Fallout (3) but I have the feeling that thise franchise can get so much better if they implement some of my suggestions.
PS. Fallout in Europe is also awesome but not as a sequel. Maybe a spinoff series (Fallout: Europe) would be cool to expand the lore with what happened and goes on in Europe)