NYE, would be busy and packed everywhere so might be difficult to get a place unless you book in advance.

There will be food at Changi Village so no worries. Or as mentioned, if you really want Ya Kun there is an outlet in the basement of White Sands just off Pasir Ris MRT station. I live around here and there are other local food options (beehoon anyone?) in the stalls under the MRT if you don't feel like having toast this morning. Or Old Town White Coffee on the first floor of White Sands; though I like Yakun a lot more.