If you want authentic Sri Lanka cuisine, head to the Garden Cafe. It is located just by the lakeside and is a tiny little place (so seating is limited). Many of the locals use it for take away. The food here is very good (albeit spicy - so take care if you are sensitive to spices) and very affordable for any traveller. The menu is quite large, although they may not have everything on the menu towards the later evening. Try the Kotthu here - it's very nice.
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