Following is mine itinerary for Israel in May, please add or subtract as you see fit!
Day 1 Thu Arrive TA at 9:00 am TA, Jaffa overnight TA
Day 2 Fri Am TA, pick up rental, Pm Caesarea overnight Haifa
Day 3 Sat Haifa, Megiddo overnight Haifa
Day 4 Sun Akko, Rosh Ha-Nigra overnight Haifa
Day 5 Mon Nazareth, Cana, Mt Taba, Druze Village, Zippori overnight Tiberias
Day 6 Tue Ginossar, Tabgha, Capernaum, Korazim, Kursi, Yardenit, Magdala overnight Tiberias
Day 7 Wed Metulla, Golan Height, Mt Bental, Bental Davidson Center, Gamla overnight Tiberias
Day 8 Thu Qumran, Jericho, waterfall overnight Ein Gedi
Day 9 Fri Am Masada through Snake Trail, return rental car in Jerusalem around noon, Pm Bethlehem overnight Jerusalem
Day 10 Sat Hebron overnight Jerusalem
Day 11 Sun Am Kotel Jerusalem and overnight
Day 12 Mon Jerusalem and overnight
Day 13 Tue Jerusalem and overnight
Day 14 Wed morning to Amman throught Allenby overnight Mataba
Day 15-21 Jordan
Day 22 Fly home
I have not figure out the itinerary for Jerusalem yet so any suggestions would be very helpful.
If needed, I could cut one day in Jordan and use that for Jerusalem.
Would you recommend taking bus to Elliat and cross over to Jordan from there and work my way back to Amman?