No worries about finding coffee, but the crowds could be a problem. Outside the park there are other places that might work for you.
Yes. There is a very nice one in the park which seems to be a good restaurant as well. We had there just coffee and cake. Located at the front of a small lake with ducks.
There are 3 in the park and they are signposted. 't Blauwe Theehuis, De Vondeltuin and Groot Melkhuis. Many others are close by. Go to Vondelpark on Google maps and type coffee shop in the search box.
Best time to visit is April.
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