How widespread is public wifi in hotels, public places, coffee shops, trains, buses, or even whole cities in Israel? Also, are they generally password protected (like many coffee shops in the USA)?
The amount of free wifi in Israel is ridiculous. Egged buses have it most of the time. Gas stations (at least Paz and Dor Alon) have it. Tel Aviv has municipial wifi. The list is endless. I had the good luck to never need a password. Others might have a different experience, I guess this differs from place to place.
in Tel Aviv ,Jerusalem and Haifa you have free Wifi provided by municipality. Their speed are not greatest but you can download your mails and chat on your whatsapp, also most of the coffees has usually free wifi for clients.
I would add that hospitals in Israel also have free - non-password protected - Wi-Fi. And free recharging stations.
(I can't guarantee that ALL of them do, but so far I haven't found one that doesn't.)