Am happy to see you are going to Limassol. If you are hiring a car and planning a day to Paphos I would advise leaving quite early and using the old road which is the sea front from Limassol going through the plantations of Akrotiri area and passing Curium (Kourion) (a place worth visiting in its own right with the amphitheatre and good beach with tavernas.) I also like to visit Pissouri but that should be on a separate day or you wont have long enough to see Paphos. By keeping to the B6 you will have the wonderful view of Aphrodite's Rocks at Petra tou Romiou. I always like to have a drink on the terrace of the CTO restaurant which is signposted turning right before the Rocks, the road leads upwards and when you go through the restaurant you get a wonderful view of the rocks from above the road. There is car park on the right hand side right opposite the rocks but without a good view or taverna.
As for eating places in Limassol do try Mikri Maria's in Ankara Street near the Castle/St.Andrews Street area. Her food is always excellent and you get the impression you are in her dining room it is so homely. I have met many Cypriots there because they like her food. The menu is good Cypriot cooking and I love her grilled fish.
Outside Limassol my favourite is Kamares in Lofou Village.