The only advantage of connecting flights is that you can at least step out to see whatever little you can. At least get the flavour of the city. Yes, not the ideal way to explore. But, well its worth getting a break.
[A tip: try to have your journey breaks in the same city.]
One our way to Iceland, we had a stopover at Amsterdam, well KLM flight. And here's what we did.
1. We took a train to the city centre.
2. We walked around to nearby cafes and found an awesome place to have breakfast.
3. We got ourselves enrolled for a river cruise - that would give us a quick tour of the city.
4. We returned in-time to the airport, after spending some time at the duty free.