I've had some marvellous free 'concerts' recently.
First in St Giles' cathedral, Edinburgh, where a young lad was playing the Rieger organ. Subtle, that instrument is not! But it's massive, and rather great, and he was pretty good, too.
And then at the east end of Regensburg cathedral, where the 'Domspatzen' were having their rehearsal on Sunday morning, and had left the door open because of the heat. I sat down on a step nearby and listened for half an hour or so.
It's nice when you get a spontaneous free concert like that. But more formal free concert opportunities are also worth looking out for. Many churches in the City of London have a free lunchtime concert - St Anne and St Agnes in Gresham Street does; it also has a Bach Vespers many Sundays, at six, with professional musicians performing Bach cantatas as part of the liturgy. Very highly recommended.
Church services aren't always a musical feast. But most English cathedrals, and the major Oxford and Cambridge colleges, have good choirs providing regular sung services. Watch out though as they have one day a week off. For instance at King's, Monday is a day off, and on Wednesday you will hear only men's voices - that is, the boys are not singing. King's also offers an organ recital on Saturdays at 630 pm, with free admission.
In Paris, Saint-Eustache has a monstrously capacitous organ and there are regular free recitals, at 530 every Sunday; Saint-Merri and the American Church (each Sunday at 5) also stage free gigs in summer.