If you are a football fan you may want to buy a Hajduk souvenir. There is a Hajduk fan shop conveniently located in the old part of Split just off Marmontova.
For the pin collectors I have to say that there is no proper pin available unfortunately.
What to buy:
There is some okay shopping in Split. It is not as commercial as a lot of European destinations, and therefore doesn't have the shopping that some do. However there are some very nice little shops. Split is a lot less expensive than a lot of places in Europe.
It doesn't seem to have a specific thing to buy like some destinations. A lot of the items are cheap and badly put together, and not things that you would want to give to people on your return.
Nobody spoke English, but the people were generally very friendly and we made do with some hand gestures (the polite kind).
The money is odd, you can't buy it before you get there and I struggled to keep it straight in my head compared to other currencies.
The market is okay. It has a whole range of items, again very cheap etc. I did find some nice baby clothes that seemed decent.
It has a lot of nice cafes etc. but you need to be aware that the lot of them smoke like chimneys - in or out, and it is difficult to find somewhere to sit and have a coffee etc. where you aren't suffocating in cigarette smoke.
Definately not wheelchair friendly.
You can purchase souvenirs and trinkets from the souvenir stands in Diocletians Palace, if that is what you are looking for.