It can be a tight fit and some of the more crowded spaces and I think it would get in the way. I do not know if they have a strict policy against it or not but that's my opinion
You can definitely keep your bike with you at some of the tables, they are quite spaced out. The only problem that comes to mind is when ordering, you will need to secure your bike as you need to go inside and order as well as well as pick up your food.
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