If I were you, I'd go to the Old Town of Jaffa in the morning. That's my favourite part of seaside Tel Aviv. I spent a morning there once when I arrived at 2AM.
If you arrive at the Central Bus Station in Jerusalem with a bus from Tel Aviv, the easiest way to get to Bethlehem is to take a bus to Gilo and walk from there to the checkpoint. I did that a couple of times, and it's only a 5 minute walk from Gilo. I think you need bus number 31.
If you're in the Old City of Jerusalem, you just exit the Damascus Gate and take an Arab bus from the bus station there to Bethlehem.
The most interesting sights at the Dead Sea would be Masada and walking in the Ein Gedi Nature Reserve. The buses are very infrequent, so it's better to have a rental car or join a tour. For "swimming," I'd recommend Ein Bokek beach in the southern end of the Dead Sea.