The restaurant inside the gardens is available most hours. The food is delicious and reasonably priced.
I believe you can picnic just about anywhere outside, if you're looking for something outside of their awesome Cafe!
As others have mentioned there's the cafe which is very nice but pricey. Or you can bring your own food and eat on the ground but be aware you can only eat in designated areas you can't just have a full-on picnic anywhere. You'll be safe though if you see a picnic table that that is a good place to have your lunch.
They have a restaurant/cafe inside the main building. We have always brought something and ate somewhere on the grounds.
Good food though the cost are a little bit high.
Cafe in the gardens
They have a nice cafe right at the gardens.
Cafe is available.
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