On the NX-01 Enterprise ("A Night in Sickbay"), Hoshi is taken to task by a bureaucrat for not changing their on-board clocks to align with planetary local time. He is displeased at having been woken in the middle of the night:
KREETASSAN: [on viewscreen] Why haven't you adjusted your time to our capital city?
HOSHI: I apologise. We weren't aware that it was required.
KREETASSAN: [on viewscreen] It isn't a requirement. It is simply a courtesy. Something your species doesn't seem to understand.
HOSHI: I'll explain it to the Captain immediately.
It makes no sense for individual planets to maintain Federation Standard Time so I think we can reasonably assume that for anyone who intends to deal with someone on-planet, that you would simply maintain your usual day/night cycles and timezones.
If you had any dealings off-world there would presumably be a second clock on the wall marked "Federation Time" which would show the time at Federation HQ, San Francisco.
If one is in doubt of the time (perhaps as a result of a temporal anomaly), you can always access a Federation 'Time Beacon'.
In numerous episodes (TNG: "Chain of Command, Part I", "Data's Day" & VOY: "Night", "Warhead", "One Small Step", "Renaissance Man", "Author, Author") we see that Starfleet ships tend to maintain a 3-shift and occasionally 4-shift shift rotation off a standard 24 hour clock. The exception to this is DS9 which maintains a 26 hour day in line with Bajor (DS9: "The Assignment"; DS9: "Starship Down, DS9: "Accession"). Despite this, we never see the crew schedule any activities to happen between 23:59 and 25:59 local time :-)
Given that only unexpected events occur during the 'Night Shift' (a Borg attack in VOY: "Survival Instinct" and a Magnetic Constrictor Explosion in VOY: "Investigations") it can be reasonably assumed that other Federation ships, even those from other worlds also maintain UFP time.
On a personal note, I like to think that Harry Kim has one of these in his quarters...