I stayed at Backpackers Fairytale Hostel. It's a cute, clean hostel and although it is relatively small, the cheap price and location made it well worth it.
The Diocletian's Palace is a major attraction in Split. I spent a few hours exploring it and going into the museum. The palace is in the middle of the city with businesses built in it. There are plenty of tour guides around though I chose to explore the area myself and read the signs posted.
There are lots of affordable bakeries in the area where I chose to get my meals, at just a dollar or two for a loaf of bread or other fresh pastries it's hard to beat!
Later in the afternoon, I hiked up Marjan, a hill the overlooks split and the Adriatic Sea. It's an easy walk with a slight incline and there are paved paths going most of the way up (see picture for view from Marjan).