Favorite thing: Split is known to be a gateway to the Dalmations and in the summer months it's often packed with travelers using it as a jumping off point or a base of exploration for the surrounding region. There are many islands that you can reach by ferry from Split on day trips, including Brac, Hvar, Vis, Korcula and others.
Get on a boat and pick your island for the day. From Hvar, there are a countless number of islands, big and small, to which you can hop. Some of these have some kind of amenity, such as a cafe or small store, but most are just semi-secluded beach islands where you can while the day away in brilliant sun.
Fondest memory: Swimming off the rocks at Sveda Ndlja. This remote corner of Hvar features a 50 meter promontory on which a lone Cypress stands. Imposing cliffs descend into a deep crystal clear lagoon. From the surface of the bluish water you can see all the way to the rocky bottom -- about 50 meters in all. Freaky. In a good way. Another memory, definitely NOT my fondest, but certainly among my most memorable, was flying into Split airport and seeing all of the fire control planes reloading water from the Adriatic for another pass at the brush fires on the islands. This happens sometimes during dry years. Quite tragic, as the vegetation on the hills adds a lot of character to the rocky scenery.
Favorite thing: Most people come to Split as a passageway to the Islands of Dalmatia and for Dubrovnik. For the islands the ferry service is essential, and offers some of the best views of Split and the islands. For Dubrovnik, the ferry skips through the islands at a leisurely pace, if you want to arrive in Dubrovnik quickly and probably more comfortably (unless you book one, you don't get a seat on the ferry) its best to take a bus (around four hours travel compared to the ferry's seven hours). You also get a bit of Bosnia-Herzegovina thrown in for free (with border guards of course).
Komiža is 2 and a half hours from Split by ferry. Start drinking beer on it...
Fondest memory: Just enjoy in the color of the sea.