I got it:
...before it gets too commercial and prices skyrocket!!
It dates back to the 7th century (so you can count on the old town have beautiful fortresses and cobbe-stone streets) and located on the Adriatic Sea (so you do get your beach (which I've been on), yet you might have to sacrific the coconuts (although somehow I do remember palm tress there).
I've been to over 55 countries, yet somehow Dubrovnik still stands out in my mind.
PM me if you'd like further info.
ETA: However if your energy's low and you want to do the beach thing drinking out of a coconut and sightsee a little, might I suggest a one-week all-inclusive in Cancun (sightsee the Mayan ruins). There you can also swim with the dolphins if that interests you. I see you're in the US so the flight's not too far for you as well.