Can Accelerator be killed by a nuclear weapon?
I would assume that he would have no trouble deflecting the initial blast because it's just a straightforward shockwave (no dark matter shenanigans here). But there's more to worry about than just the initial shockwave.

During Accelerator's fight with Touma after he sets off the dust explosion, he actually does contemplate on such a scenario. He notices that the temporary lack of oxygen from the dust explosion almost killed him, and comments that he probably wouldn't be able to survive a direct nuclear blast for the same reason. In the novels, he considers the idea of oxygen tanks to remedy that problem, since some are made the size of hairspray bottles.