Gozo is the often forgotten about island in the Maltese archipelago, but I think it has so much more to offer because it is generally quieter than the larger main island. Access is via a short ferry ride from the northern tip of Malta, and goes past Comino, famous for it's Blue Lagoon. The crossing often allows for views of dolphins and sometimes sharks, so it's always worth being up on deck (minus the sun hat unless it's tied on!) The ferry arrives in Mgarr, and from here the island is easily accessed using public transport. The main bus terminal is in Victoria, in the centre of the island and with some forward planning you can see a good deal in one day.
The Azure Window and Inland Sea at Dwejra are a must see for natural spectacles. The geology is amazing and numerous fossils can be found in the rocks. When the weather is good, there are cruise boats that go along the coast and explore some of the caves and inlets. While the buses run fairly regularly, if you have time to wait, there are a couple of nice gift shops selling local glass wares and a nice restaurant.
Between Dwejra and Victoria there is a Craft Village at Ta'Dbiegi which supports local crafts such as lace and leather, glass, pottery and candles, as well as food. There is also an impressive Church on the way called Ta'Pinu, which stands alone in the impressive limestone landscape. Victoria being the main city on the island, it has the usual Maltese architecture mixed with modern-ish shops. To escape the hustle and bustle of the main streets, head up to the Citadel, where there are a couple of museums and the Cathedral to have a look at, as well as panoramic views of the whole island!