The best decision we made on our trip to Croatia was to stay in the Old Town.
We were constantly popping in and out of our apartment, snacking, grabbing more money, changing shoes/bags/clothes. It made our trip a lot more spontaneous not to mention convenient! If you visit Dubrovnik please stay in the Old Town, it might be a bit more costly, but it's so worth it.
It means you get to see the local's Dubrovnik which is more like this: