Who knows of quiet and romantic places for or what to do on a first date (in Mauritius)?

The first part of your question has already been discussed here.

The second part, however, is subjective. Teenagers may prefer to go watch a film together while young adults may find going on a lunch/dinner date better. The older generation may find sitting on a bench near the seaside/botanical garden more suitable for them.

When going on a first date, the most important thing is to make it enjoyable by both persons. So you need to know what the other is into first. Then conversation is the key.

I prefer nature walks where I'd get the opportunity to know the other person better...