Tourist places and shopping centers are all open.
Only govt and offices are closed.

Indian:
Banana Leaf in little India seems popular.
I know some native Indians who like Gandhi restaurant, also in little India.
Both are not fancy type places.

Japanese:
There is a very good ramen restaurant in Plaza Singapura, beside Nana's Green Tea(which is quite good by itself and has a value set lunch).
Their ramen is quite different, in a good way.
Cant remember the name but it is just beside Nana's.
Saw a lot of expat Japanese eating there as well.

Ramen Champion is recommended too and they have several locations.
Havent tried it though.