This is really a tip about taking care of the clothes you have packed, rather than what to bring with you.
At last! a laundrette has opened in Split - the first in Dalmatia - and as it is just a stone's throw from the Riva, really easy to access. It's the brainchild of an enterprising Australian couple from Perth (they run tours and sea-kayaking adventures as well) and they offer a whole range of services aside from taking care of your laundry. As well as self-service and fully serviced laundry, you can check your emails and leave your luggage here for a few hours as well as have your questions about Croatia answered by the friendly and helpful staff.
They're open every day in the summer season (April -October 0800-2000) and 0900-1700 Monday to Saturday the rest of the year.
You'll find them behind the Franciscan church at the opposite end of the Riva from the port at Sperun No 1.
Miscellaneous: Our surprise was great when we discovered the number one issue of the the Split In Your Pocket guide. It was a free copy and we actually got it in the tourist office in Supetar on Brac island. But you may enquire at the tourist office in Split whether they have any.
If your feet are sensitive I suggest bringing shoes to wear in the water since the bottom of the ocean is mostly rocks.
Camping/Beach/Outdoor Gear: If you plan on laying out at the beach, I recommend you bring something padded. I was surprised not to see a sandy beach but most of the beach was build out of concrete. The water was shallow for quite a distance so it was nice to play ball or hackey sack.
The summer months can be brutally hot here in Split, but the winter is relatively mild. I was here in February and it was pleasant in the daytime, and pretty cold at night (0 -10 degrees celsius or so).
The Old Town streets are old and sometimes you'll find uneven pavement, so be sure to bring comfortable shoes.
Photo Equipment: Of course, you'll want to bring your favorite photo equipment. An almost 2000 year old Old Town, a backdrop of snow-capped mountains and a beautiful bay are all worth your camera's attention.
Miscellaneous: After Yugoslavia. A book by Zoe Bran is great reading, either before or during your trip. Lots of information and history, both recent and long ago, I found it helped me to understand the region. Easily the best travel book I've read lately. It's published by Lonely Planet.