Jerusalem is in the Judean hills. The closest diving is in the Mediterranean Sea, roughly 30 miles away. Some sites are very unique, but this is going to be low-regular visibility. Don't expect a coral reef.
Eilat is about 4 to 4 1/2 hours by car or bus and it's a very scenic ride. It takes you down the the hills, by the Dead Sea (there is a 10 minute break on the bus) and by the Arava valley. Eilat is the northernmost part of the Red Sea. In my opinion it is worth the ride or drive. I suggest taking a bus or renting a car. The airports (Sde Dov and Ben Gurion) are in Tel Aviv. It would take time to get there, plus security.... I don't think there are flights anymore from Atarot in Jerusalem.
From Tel Aviv, there is an overnight bus. There may be one from Jerusalem too. Worst case, you take an overnight bus down, dive for 1 day, stay overnight and go back the next day.
