In ’95 when I went to Israel, I got a chance to see how well-coordinated the outreach workers are. There seemed to be several entry points for a person.
Chabad has an outreach office on the Cardo. Jeff Seidel goes to the Kotel every Eruv Shabbat to assign visitors with appropriate hosts for Sabbath meals. And also, Heritage House serves as a youth hostel. Al of this is not done without great care.
Diaspora Yeshiva allowed me to sleep on their campus while going to Aish HaTorah for a while but eventually I had to go to Diaspora and I documented certain problems at that yeshiva both recently and years ago on this forum.