Amata's still reconciling herself to being the leader of a much smaller community. The new president should already have leadership experience. Here's a list of persons who do. I chose to be as comprehensive as possible, I'm not saying all of these people would be good choices. But they are experienced leaders.
Overseer Almodovar
Lucas Simms
Harkness
Dr. Li
Bannon
Dave
Col. Autumn
Elder Owyns
Protector Casdin
Robert J. Macready
Winthrop
Alastair Tenpenny
Eulogy Jones
Let me slowly pick away at your suggestions! The overseer of vault 101, Mr.Almodovar! No, he's a raging pshycopath who can barely manage his vault, let alone the entire country.
Lucas Simms... hmm, he seems valid, I don't know though.
Harkness - well let me put this in here
Spoiler well lets see here.. he's a robot for one thing, he can only do what he's programmed to do. theres also the small problem of being an andriod ( even though he's the most advanced one ever! he's still an andriod/robot/computer, and we all saw what happened with that...
Dr. Li - as of B.S. she is back in the commenwealth doing research! She is more interested in scientific pursuits rather than political ones.
Bannon - He's a liar, he tried to convince all of rivit city he was it's founder, and failed miserably at it.
Dave - He's a dictator, we wouldn't want that running the country, now would we?
Col. Autumn - Well I support him, he wouldn't be all bad..
Elder Owyns - Again, I'd support him.
Protector Casdin - Clearly more caring about preserving technology, not humanity, and is more in line of the brotherhoods original goal, and they had the power to reorganize and take control over the country, but didn't. bottom line is he would be a horrible president, he wouldn't care about his people!
Robert J. Macready - he's a kid! maybe when he grows up but I highly doubt he'd make a suitable president.
Winthrorp - he's a mechanic for gods sake, and a ghoul, who will eventually turn feral!
Alistair tenpenny - Well he's a crazy old homicidal man, who had no problem with nuking an entire city, and enjoys "wasteland saffari's " where he kills people walking around nearby his tower.
Eulogy Jones - He's a slaver! Come on really?! he has no morals OR ethics, he would probably become a homicidal dictator out for money!
Well that's all for now lol just figured I'd chime in.