Kirk, Spock & Scotty have gone bowling.
Not quite. They wish they had, though. Well, maybe not Spock. The others, though, come pretty close to regretting they left the ship.
What time period is this set? Within the 5 year mission?
Straight in the middle of the 5YM, yes. Early-to-mid 2268, in fact.
Where are Kirk and Spock?
Definitely not in a bowling alley. They're doing a bit of exploring off-ship, but there's Trouble waiting for them. See our Unreality SF interview from last year
; the first half includes some more information about the novel.