A nine-hour layover sounds generous until you subtract two hours for immigration and security on re-entry, forty minutes each way into the city, and an hour of buffer before boarding. That leaves roughly four hours of actual time. Below that threshold, staying airside is usually the better decision, and above it a short trip is genuinely worthwhile.
Count the buffer before the fun
Work backwards from the boarding time and be strict about the return buffer. Security queues on a busy evening can run longer than the outbound journey, and a missed connection on a separate ticket is expensive. Set the return time by the worst realistic queue, then see what remains. If it is under three hours, stay put.
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Keep the plan geographically small. One neighbourhood with a market, a park and somewhere to eat beats a list of three sights, because you will not have time for transport between them. Choose a district a single train line from the airport and stay within walking distance of the station you arrived at.
Lounge access and a city trip cost differently
Compare the cost of a day pass at an airport lounge against transit, a meal and any entry fee in town. For a four-hour window, the lounge is often cheaper and certainly more reliable, especially in poor weather or after an overnight flight. The city option wins when the window is six hours or more and you are rested.
Actionable step: before booking, check whether the layover airport requires you to clear immigration even when staying airside, and whether your ticket permits re-entry. Some airports and some visas do not allow leaving transit at all. Confirm both before planning anything, because neither is fixable at the gate.
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Baggage rules decide more than timetables do

Checked bags are usually held by the airline, which is convenient, but some airports require you to collect and re-check them. That can consume an hour and makes a city visit impractical. Carry-on only turns a long layover into a real opportunity, and it is the single change that most improves the maths.
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