Depends on the episode.
When Quark is abducted from Deep Space 9 in "House of Quark" he's taken clear across the entire Federation and into the Klingon Empire in about a day. And then D'Ghor sends someone to the station to grab Rom and get him back to Qo'noS the next day.
Trek moves at the speed of plot.
I wouldn't say they're exactly logical....