Based on these response, we will definitely rent a car.
Israel, outside of Jerusalem and Tel Aviv did not strike me as easy to get around without one. Of course if you have a tour guide you won’t need to.
We used this guide: www.dannythedigger.com for three separate day tours. He’s an archeologist by training, very knowledgeable and accommodating. His site will give you ideas for day trip itineraries. When we met up with him he gave us a rundown of what was possible (logistically) to see that day and we picked the things we were most interested in to focus on.
The food was generally amazing.
Not that you would, but don’t skip the Garden of Gethsemane. The church there is beautiful, as is “Mary’s Tomb” nearby. Magdala is also beautiful; I had never heard of it and would have skipped it; I’m glad I didn’t. If you find yourself in Tel Aviv the Art Museum is very good and worth seeing.
You’ll have an amazing trip.
No specific hotel or guide recommendations since my time there is 25 years out of date. I do, however, recommend getting a car for maximum flexibility. The drive from Tel Aviv to Jerusalem was very enlightening with things like some of the vehicles from the '48 war still there to see.
There used to be some issues with getting Israeli stamps in your passport and finding that they would limit its use in other parts of the region ... may want to check that out.
They print off a little sticker with your picture, and, I think passport information and you’re supposed to carry that with you. I did and left my passport in the hotel safe.
The weather was just about perfect. I recall only wearing a light jacket 2 days. It was pretty much Dockers or jeans with a long or short sleeve shirt the rest of the time. Remember to pack a bathing suit for the Dead Sea.
I've linked the itinerary to give you some ideas on what to see. I was part of a tour group, but it appears you'll be touring on your own. As such I suggest you contact this group as they can probably recommend guides for you.
You'll also notice the hotels we stayed at are included in the link. They're all 4-5*, and all meals are buffet style (think Vegas for quantity). The selections are always a mixture of American & Israeli cuisine and all were excellent.
One other thing I liked that hadn't occurred to me. It wasn't necessary to get Euros as every place we went accepted American $.
Enjoy your trip.