May is better than April if you fancy sunbathing on a beach however it might still rain. It also gets ever so busy with families with children as this is when school holidays are. So avoid the end of May unless you are also travelling with kids and can't go later in June for instance. Split is a wonderful choice! I suggest spending a few days in town, explore the Diocletian's Palace, etc. then hop on the ferry to the island of Hvar. Many flock to Brac, the sandy beach, rest are pebbly or rocky. Korcula is also great to visit as it also has a fantastic Old Town but it's further away. If you just do Split & Hvar for example you can easily do without hiring a car. A must visit at least as a day trip is the Plitvice Lakes National Park, book a full day tour with pick-up and drop-off or just drive there, it's about 2 and a half hours from Split. Have fun!