Elizabeth Warren, Tammy Baldwin (assuming she survives 2018), Kirsten Gillibrand probably.
Elizabeth Warren will be 75 years old. Doubful she'll be running at that age.
I do think both Gillibrand and Klobuchar would stand a good chance of running, as they both seemed to want to run this time around, but couldn't because of Clinton.
I don't know though. I'm guessing the majority of candidates will be people who don't yet hold statewide office, as of now in 2015. Though whoever the vice president is will presumably be someone who we already know right now, and I'd assume they'll probably run for president in 2024.