Ann, it's a long time since I was in my 30s, and here's a report of the hostel in Shlomi, where I stayed two weeks ago. Shlomi isn't on the tourist trail (it's north of Nahariya, just south of the Lebanese border), but the hostel is typical of Hostelling International hostels in Israel.
I had a double room (I travelled alone), with two single beds - widely spaced, fine for two friends but probably not what a honeymoon couple would want (!) - my own toilet and shower, a fridge and coffee-making equipment in the room, a TV, tons of storage space, and a balcony. A huge breakfast is included in the price. As it happened, when I was there there was a large group of middle-aged teachers (I was asked if I was "with the teachers' group"), as well as other guests considerably past the age of 30.
Of course there is no guarantee of who might be staying there tomorrow or next week, or in another hostel.
See here for HI hostels in Israel:
Oh, and 10% discount with a membership card, which will pay for itself after two nights. Get a Hostelling International membership card in your own country. They are valid worldwide.