First of all, perhaps a room that you can build outside of the vault for new invitees to the vault to stay in. I've had a huge waiting line for days and it seems unlikely that people could survive comfortably and just wait there. I also believe that it breaks cannon a bit. You could choose to have it look like a cave (as Vault 22), a Mechanic (as Vault 112), a storefront (as Vault 21), or others as deemed appropriate. These could have various effects on gameplay in a passive way, such as a cave having a +5% chance for Molerats to attack randomly, but a -5% chance for Raiders to attack, or the Storefront having a +5% chance for raiders to attack, but a +5% gain to caps. Numbers would have to be adjusted obviously.
Secondly, I think there should be more robots available, such as Protectrons (added vault security, perhaps automatically converging on Raiders/Deathclaws, etc), Robobrains (Passive Intelligence boost to all Dwellers in the same room?) and Mr. Orderlies (Like Mr. Handies, but they do not engage in combat, instead healing Dwellers outside of combat.) (Yes, I know Mr. Orderlies are not Cannon, however I saw them in a FO:NV mod that allows you to build and upgrade your own robots and I like the idea.) I'd like to also see the ability to upgrade your robots with materials found in the wasteland with a Robot Maintenance Bay. You shouldn't be able to build new robots like that, however you should be able to assign a robot to one and get options to repair or upgrade one. You could be able to install mods such as Laser Targeting (+10% dmg taken to the target from other sources) on a Protectron (recipe could include any kind of Laser Gun) or turning a Mr. Handy into a Mr. Orderly (Recipe could include 10 Stimpacks and 10 RadAways).
Thirdly, Dwellers should be able to find parts as items like in the newer games, such as crutches, lead pipes, motorcycle motors, etc. These could be used to stock the Robot Maintenance Bay for repairs and upgrades. This could also be used to repair Androids, such as Harkness, as an alternative to Stimpacks.
That's my list so far. If anyone has anything to add or anything they'd like to change in my ideas, please go ahead. Variety is the spice of life after all.