I was able to wait outside. There is seating but it was too hot at the time so I stood in the breezeway. Infrastructure is old but things are clean and I do think the city is low crime. I would feel safe walking around at night.
Bethlehem doc said he has seen pretty much only Russian patients. Israelis cannot enter west bank tier A zones, Jews shouldn't enter because they're at danger of being killed. Many Palestinian Christians have left due to international church support and resources, and the city population is becoming more and more Palestinian Muslim as people leave cities like Hebron. There are actually many Russian Jews in Israel so we had my fiance wear his cross to be safe, but it was probably unnecessary. Both Palestinians and Israelis try very hard to not involve foreigners if there ever is violence. Another reason I suggest Bethlehem over Ramallah is that Ramallah seems less stable. And this is if you cannot do the medical in Jerusalem. Assuming you have to leave and come back for a 221g or any other additional screening, I would absolutely 100000% recommend not setting foot in west bank.
Bethlehem has an extremely tourist-driven industry which was hit hard by covid and recent legislation. They love seeing tourists. It is probably the only tourist-driven city I've been in that doesn't hate tourists.
Taxis will be hard to source but if you get an AirBnB they'll usually get fam from Jerusalem to drive you around for like $100 lmao, Israeli taxi drivers cannot take you to Bethlehem. Always have a backup plan or arrive 1-2 days before any appointment. There is a refugee camp in Bethlehem that can be raided, and raids usually mean you cannot enter or leave for a period of time.
Gunshots from 5-9 pm are locals, gunshots from 1-4 am are IDF (which we never heard). There will be a call to prayer every night at like 2-3 am, if you are a light sleeper, close the windows.
Jerusalem is nice too, but consider renting a car while there. All affordable accomodations for us in West Jerusalem was in surrounding suburbs, and as tourists we couldn't obtain bus passes.
I did not enter East Jerusalem but from what I understand it can also be subject to raids and clashes. Cheap lodging though.