A relaxing week in a very pleasant hotel, with the beach right outside the door and reasonable accessibility to a fabulous city.
Key thing to think about is location. Split city centre is a half hour bus ride (traffic can be heavy) and buses run every half hour. If the ancient (and really beautiful) city centre is really what you're there for, then stay in Split itself. If you don't care about seeing that, and just want the best possible beach, then there are probably some island locations that give you more idyllic beaches. But, if you want reasonable access to the city, and to lots of other places by bus, as well as a good-enough beach on the spot, then this is highly recommended.