Sitia will be just about the closest, but Ag Nik would be a better bet, providing you've got transport.

near by there are some accommodation in the area, that belong to the monastery, but are run after another company/individual.
dont know if nice, dont know if good or how close. all i know is that they exist.
still though better option for me is Sitia as mention above

Sitia will be your best bet.

There are plenty of rooms in Palekastro, which is closer to Vai than Sitia. It's a firendly little town and has got a nice beach of its own which is a lot less crowded than Vai. There are buses to/from Sitia and Vai a couple of times a day.

I'd stay there.