Chez Eugene is in a small town in the Negev -- Mitzpe Ramon -- that is home to Israel's largest crater, Makhtesh Ramon (which you can and should hike in!). It's a modern boutique hotel with very chic rooms and a helpful staff. Given how small and intimate it is (I believe there are 6 rooms total), it seemed more ideal for adults than children, though the manager mentioned they often have families come and stay. We spent three days in the area, and it was one of my favorite parts of the trip - we hiked around the crater, swam at recently opened hotel in town (Beresheet) and had dinner at a local joint that a fantastic beer selection (Hachavit).
Shalom Hotel & Relax is conveniently located on the beach in Tel Aviv and was similarly intimate and chic. The rooms were comfortable (if not a bit small) and the staff was super helpful in recommending things to do and see around Tel Aviv. We heard breakfast is quite good, but skipped it to go to Benedict's around the corner (which I can conclusively say has the best Shakshuka in Israel -- we tried many!). There is also a beautiful rooftop patio that was the perfect place to watch the sunset. Highly recommended!