The best time to extend a city break is before checkout on the morning of your last planned night, not after. The hotel, the airline, and your options all get harder once you've left. Act while you're still in the building.
The Hotel Extension: Call Before Checkout
Go to the front desk or call down from the room before you check out. Ask whether the room is available for additional nights. Most mid-sized hotels will be able to tell you immediately, and many will hold the same room rather than moving you.
The rate for additional nights booked this way is sometimes the same as your original booking and occasionally higher (walk-in rates can be). Ask what they can offer before agreeing. If you booked through a platform originally, the hotel's direct rate for the extension may actually be lower. It costs nothing to ask both.
The conversation takes five minutes. Waiting until after checkout and trying to rebook means going through the platform again, possibly losing the room to someone else, and definitely having to check out and check back in.
Changing the Return Flight
This depends heavily on how you booked. Flexible fares allow date changes for a fee that's usually modest (20-50 pounds on most budget airlines). Standard fares on Ryanair, easyJet, and similar charge more for changes and may cost you close to the price of a new ticket.
Before paying the change fee, check Skyscanner or Google Flights for a new one-way ticket on the return date you want. If the new ticket is cheaper than the change fee, buy the new ticket and accept losing the original return flight. You'll need to check that the original booking doesn't include checked luggage you've paid for separately.
The Two-Night Extension
Two extra nights is the extension that transforms a weekend into a proper trip. A Friday-Sunday city break extended to Friday-Tuesday gives you time to slow down, go back to places you liked, and have an evening without the background pressure of leaving tomorrow.
If the city has earned the extension, and the hotel can accommodate, two nights is the right ask. One night feels slightly too short to change the shape of the trip; three starts to require more significant flight and cost recalculation.
When the City Hasn't Earned It
The extension should be a response to the city pulling you back, not just inertia. If you've done what you came to do, if you've found it slightly disappointing, or if you're mostly avoiding the reality of going home, the extension rarely fixes that. A comfortable home flight and a good night's sleep is a better decision than two more days of going through the motions.
Stay when the city has given you reasons. Leave when it hasn't.
ConciseTravel