At a time like this, there's nothing like a morning-after drink.

Literal

This-kind-of time [topic-は], hair-of-the-dog [to-に] is-limited.

A casual recovery line. 迎え酒 (むかえざけ) is the Japanese term for 'hair of the dog' — literally 'welcoming sake' — an alcoholic drink taken to cure a hangover. The pattern ~に限る ('there's nothing like X,' 'X is the best') attached to a noun expresses that X is the ideal solution or preference for a situation. Common opener: 暑い日はビールに限る ('on a hot day, nothing beats a beer'). ~限ります is the polite form. Together: 'for this kind of time, hair-of-the-dog is the only thing.'