Things to know: If you are going to be in Israel between May 7-9, let me know. I'll give you more information. There is little public transportation on Shabbat - mostly taxis and shared taxis ("sherut") on some bus routes, except in Haifa where there are some buses. Vegetarian is easy in Israel. Nothing has meat products unless it is obviously meat. No animal fats are used in cooking except possibly butter and then only if it's stated on a menu. Baked goods are either vegan or vegetarian. If you are vegans, it's still pretty easy to avoid dairy and eggs. GPS doesn't work in Israel. Everyone (really everyone) uses Waze with a smartphone. The maps are all in Hebrew, but the directions and place names can be set for English.
Day 1 - as I said before, pick up the car the night before so you can get out of Jerusalem around 7 am, before rush hour starts. A big bus tour is not for me - getting herded around with lots of waiting to get on/off the bus and for stragglers. Masada has an introductory movie and a good audio guide with lots of written explanations as well all over the sight. Ein Gedi is a simple hike up to the waterfall and down again. Keep your eyes out for wildlife. If you're skipping Beit Alfa, do stop to see the mosaic floor at the ancient synagogue. On your own, you will have time for Kumran as well. It's a well-posted/explained site with an introductory movie. If you spend the night in Ein Gedi, they have a private beach with a shuttle bus that should be included in the price. If you stay at one of the hotels in Ein Bokek, some may have private beaches. Last time I was there, albeit several years ago, there was access from most of them to the public beach, something new since till then the beaches had mostly been private. It's possible that most places have a 2-night minimum stay. Then it makes sense to get the car in the late afternoon to drive to the Dead Sea. It may even work better for you in any case. If you "insist" on only one night, there's a youth hostel at Masada (see below for more info on hostels), which I've never stayed at.
Day 2 - You should have time to visit Bet Alfa if you're staying in Tiberias. If you want to see the ruins in Belvoir, go for it. If you are going mostly for the views, be aware that it can often be hazy and disappointing. My go-to place to stay for my trips to the north is the Karei Deshe Youth Hostel. My other one is the Poriyah Youth Hostel. These are basic hotels, with private rooms and en suite bathrooms with walk-in showers. Rooms have 2 or more twin beds, a minifridge, an electric kettle, self-controlled AC, and some have balconies. They have good buffet breakfasts (included) and usually have buffet dinners (with a good selection of vegetarian options) at very reasonable prices. Karei Deshe is a few kms north of Tiberias right on the shore of the Kinneret and is ideal for day trips to the Galilee and the Golan. Poriyah is south of Tiberias, not as good for day-tripping, but has great views of the Kinneret.
Day 4 - a little ambitious both for time and for hiking. Take good binoculars for Agmon Hahula. It's a good idea to call them to make the reservation and ask how many and what kinds of birds to expect. There may not be much to see by mid-May.
Day 5 - How much time you want to spend in Safed? Driving in and out will take time - not as bad as Nazareth, but it can be really slow. Bar'am doesn't take long and it's nice. Without Peki'in it sounds doable if you don't spend too much time in Safed. The trick is to get to Haifa before the rental place closes, unless they have after-hours drop-off.
Day 6 - If your folks have a car, that may be better for Akko. Last time I drove to Akko I parked in a large shopping mall and took a short taxi ride to/from the old city. If you take the train, then it's a short taxi ride or a longish pleasant walk. Parking around the old city is sparse. I could easily spend a whole day in Akko.
