I do not put nearly the thought into this that some clearly do, however I think a timeline just slightly after 3 is plausible, as is a timeline that takes place a few years after the events of 3. The tech seems so much more advanced than what we saw in 3, so that seems to indicate some time has passed. Also, as someone rightfully pointed out in an earlier post, Todd Howard said "some events transpire" and then we emerge from the vault 200 years later. We have no clue how long the "events" take to transpire. It could be just a few hours, or a few days, or even a few weeks or months.
If we look at 3 and out time in the vault, we had several fade out moments where large amounts of time passed. It is possible that something similar occurs in our vault 111. It could be this:
We get lowered into the vault along with our spouse and child and the few survivors seen outside when the bomb drops. Once inside the vault we are asked to see the overseer where we are asked what our particular skills are, or take a "test" to determine our skills (or maybe perks since it appears skills may not be in game per se, based on our SPECIAL stats). Think GOAT but for grownups. We are then assigned a job, and maybe we have some interaction with our spouse to help set a emotional bond between us and our family. From there any number of things could occur, perhaps a "failure" of a critical life support system that forces us into the cryostasis pods, and that could occur a few days after going inside or a few months, and then we emerge from cryo to find ourselves in the empty vault.
Of course we would search the vault for our spouse and child, maybe finding them empty, or find them (gasp!) dead. If empty, searching some terminals inside the vault may give us clues about what happened to them, or that being frozen was the plan all along for Vault 111. Further searching will turn up our Pipboy and maybe a gun and some ammo, and maybe some security armor and I bet a bobble head and a skill book or two.
Now where this puts our timeline when we emerge is anyone's guess, but I would not be surprised if we emerge late in 2277, although the weather would indicate a warmer time of year than winter. It also would not surprise me to emerge a few years after the events of Fallout 3 and the Lone Wanderer. I do not factor Fallout: New Vegas into my equation simply because it is set out west and done by another publisher. It would not surprise me however to get an Obsidian developed New Vegas 2 or other such title by 2017 that furthers that story.