Palmyrah has long been one of the best places in the city for Sri Lankan food. They've expanded well into Western and Indian too, the food is great, and it's also a comfy, quiet, chilled space to dine at.…
Sulthan Palace (formerly Rahumania) is a great spot at the Town Hall hub to get a delicious, cheap range of biriyanis, meats and even Sri Lankanized Chinese.
Shanmugas is one of the older and more reputed vegetarian Indian restaurants. They're definitely pricier than most places but the food is very good and the service is excellent.
Mathura is a decent Indian vegetarian restaurant that has been around Colombo for years, but now at a new location.