City breaks are available to Paris and Amsterdam, from Manchester Airport, but not Madrid.
I've checked prices for a 4 night break, from 7-11th September, for example, and found the cheapest for Paris to be £264 each and for Amsterdam, £300 each in total.
http://www.airportdirecttravel.co.uk/man…
As you rightly say you could have a 7 night holiday for less. In fact, at the end of Sept. my wife and I have paid £135 each for flights and 7 nights accommodation in the Malaga area of Spain.
An alternative might be for you to look at booking a flight and hotel with Easyjet. They fly to all 3 of your quoted destinations, but from Liverpool.
http://www.easyjet.com/asp/en/book/index…