Even if your days in Corfu are limited, I really suggest you to reserve your one day for the boat to Paxos and the blue caves. There are various options, such as those with or without lunch, etc. The boat leaves the port (HANGI PORT OLDUGUNU BEN NEREDEN BILEYIM) at 09:00 am and return around 07:00 pm. If your hotel is not close to the port, bus can pick you up from your hotel for an additional fee of € 5 per person. The boats stop at Gaios, which is the main port of Paxos, and gives passenger 1 to 2 hours to eat their lunch and tour the old city. As it stops there during lunchtime, it was too hot and overcrowded. There were lots of souvenir shops in the old town.
You will get a chance to get inside blue caves by boat. They are indeed a wonder of nature. Moreover, boat stops at one of the beaches around Antipaxos, where you can swim and enjoy the bluest water.