Take the train to the university town of Leiden (30 minutes). It has wonderful streets and canals, a historic university, great museums and it's just the right size to walk around.
You'll also find lots of great cafes and bars (traditional or trendy) to rest in for Dutch gin (jenever) with a beer chaser. Go in winter - it's very atmospheric and the houses are all lit up, so you can see how the Dutch really live.
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