At first I was thinking "Huh, Nothing". Then I realised what I would like to see.
Shields.
Bear with me for a moment before you point out how retarded that is. Fallout has Melee weapons. Lots of them. Which kinda get ignored by a lot of players (Why stab, smash or cut when you can blow something up?) but if you added in shields (Ranging from hunks of metal like drain covers onwards) that could resist certain ranged attacks (And be awesomely helpful in melee) you might be able to increase the amount of players that love melee.
Sure, it is a bit illogical, but I think it could work. Large lumps of metal put in the path of low caliber pistol rounds and the like would work. It would add a bit to the game.
That and duel wielding weaponry. Now, as many people love to point out, duel wielding pistols would be one of the most fucking retarded things a man could do and, in most cases, would lead to death. Yet I argue that firing a miniature nuclear warhead at a genetically modified mutant bear thing would be a fucking retarded option and, in most cases, lead to death. Since fallout runs on "Rule of Cool" we should have a few more "Rule of Cool" options.
So what would I like added to fallout 4?
Duel wielding of certain weaponry and shields.
Plus the aforementioned blacksmithing/enchanting analogues people were mentioning. Although perhaps limited so they cannot be combined so wankers who spend 4 hours breaking the game cannot go online and ***** about how easy the game is ONCE IT HAS BEEN BROKEN.
*reads up*
Some people have mentioned mounts and other forms of transport. You know what? Also good idea IMO. Although I would be tempted to say cars and bikes would do more harm then good. But riding around on a tamed giant ant, a weird mutant horse, shit like that, it would be fun. The reason I say no to cars and bikes is rather simple: If you can travel at anything close to 40 miles an hour, the gameworld will seem tiny. Plus we all know Bethesda has issues with game engines and sometimes things take a while to load. If you are moving fast, you will get the problem with buildings spawning around you much more often (Or not and world loading times will be fucking colossal. Seriously, even if a few mods that make Whiterun more interesting the loading times for that worldspace have increased 3 fold. And I have a pretty decent computer)
So, In summary:
Shields.
Duel wielding.
Mounts.
Blacksmithing/Enchanting "Fallout Versions"
That is all I think Fallout can take from Skyrim.