Requesting advice re trave to Israel
 

Can anyone offer suggestions for budget accommodations in Jerusalem or other cities in Israel? I will be traveling solo in May and like to stay in historic areas of the city where I prefer authenticity over luxury. Suggestions for other cities/sites to see in addition to Jerusalem are welcome. I am not interested in traveling with an organized multi-day bus tour group. But I would be open to hiring a guide or joining a small walking tour while there.

Also, any suggestions on how best to get to Petra from Jerusalem and advice on transportation options for traveling throughout the country?

I would love to meet with someone from TV over coffee at Panera or Starbucks who has made such a journey.