If you are looking for somewhere for that very special night out you can certainly find that in Limassol.  There are probably too many fine dining restaurants to mention spread all over Limassol.  

In the old town you have Aliada, Tia Pitakia, Artima to name a few.  A bit further along you have Maison Fleurie an excellent French restaurant.  It is in the Tourist area coming from the old port turn off at the bridge near the police station. At the opposite end of Limassol you have Terra e Mare which is a very special place.

Then of course you can find some wonderful restaurants in the hotels. For example  The Four Seasons has Mavrommatis, Vivaldi and Seasons Oriental, The Mediterranean Beach Hotel has a very good Italian Restaurant.  

If you are looking for something romantic and overlooking the sea Puesta and Liminaki (at the Amathus Beach Hotel) are right on the waters edge.Or one of the restaurants overlooking Limassol Castle the area looks magical in the evening when the Castle is illuminated.

This is just a sample of the many fine dining or special establishments there are in Limassol.

Also on the fine dining scene. Visit the Columbia Steak house in the old port area, and the Garden Restaurant also the Black Toro in the Tourist area.

Or try the Sailors Rest at the San Raphael Hotel.