It's a great idea. Most major European cities have them and it's a great way to see the place. The success of the scheme in Paris is good; not only tourists, but people in business dress, old ladies and girls in dresses use it. You can even do the last stage of the Tour de France, although the Arc de Triumph is a bit hairy!
I don't suppose you know how or when it happened?
It can range from a big pothole, bad luck or you being too heavy, so tricky to get an exact cause.
It's fine to cycle with a broken spoke so long as there's no rubbing and you secure the broken one. I did Pedal for Scotland once with a broken spoke after 20 km!