OK, I'm going to tell a little story - it may or may not be helpful, but here goes.
I made a business trip to Israel in Sep 2012 - this was about 4 months before I got into pen turning and I was not at all familiar with olive wood at the time. However a pen turning friend asked me to try to bring him some small pieces of olive wood, and I told him that I would try.
I spent most of my time in the Tel Aviv area and never found any place to buy olive wood - there might well be some good sources there, but I wasn't sure where to look and my business colleagues in Tel Aviv had no suggestions either.
I did have a free weekend, so I was able to spend 3 days & 4 nights in Jerusalem. Near the end of my first day there, I happened to find a very helpful taxi driver. We chatted a while and I wound up booking him for the entire next day. He picked me up at my hotel in Jerusalem the next morning and we spent the day touring the West Bank. We spent a good bit of time in Bethlehem, and also toured the Herodium, the Dead Sea and Jericho and got back to Jerusalem in time to watch the sun set over the old city from atop the Mount of Olives.
I mention all that just to point out that there would have been no way to experience so much of the great West Bank sites without a personal guide, so that's something to consider.
We started out at the Herodium & then went to Bethlehem. He first took me to Johnny's Gift Shop - I loved the place. Lots of carved items, beautiful jewelry and many other items - some very expensive but also a lot of inexpensive items. I spent a couple of hours shopping there and took care of a good bit of my Christmas shopping for that year in just that short time. Johnny has several licensed guides working for him and he got one of them to take me to the Church of the Nativity for a personal tour. We were able to bypass the lines of tourists who came in by bus tours to go to all the special places in the church. I got to see & do everything that folks go to the Church of the Nativity for in about 30 minutes while most people wind up spending a half day or more because they have to wait in lines. There was no charge for this guide service, but I did give my guide a nice tip. (undoubtedly the taxi driver also gets a commission from Johnny for bringing visitors to his shop, but that's ok too - the Palestinian Christian community in Bethlehem is very close knit and works together to help each other out. I was glad that I was able to help several families out that day and I had a number of nice treasures to bring back home.)
I told my taxi driver & Johnny that I wanted to buy some olive wood and asked them if they could help me out. It took a while to explain what I wanted and why - even though they spoke fairly good English, they had some difficulty comprehending what I wanted. Finally we got directions to the workshop of Munir Twemeh & this was a real treat. He is probably the greatest wood carving artist in Israel - I had purchased one of his nice pieces at Johnny's so I really enjoyed getting to meet him and watch him work for a little while. Unfortunately, he only had a few small pieces of wood on hand at the time, but he did give us directions to the shop of another carver. This man had a much larger shop and he had a big stack of olive wood limbs in the back of his shop. He let me select whatever I wanted, so I picked out about 20 pounds of wood. He charged me $200 for it - I didn't know if that was a good price or not, but I didn't have time to run all over Israel looking for more. My friend was quite happy with it, so it all worked out ok.
So, now that I've had that experience and also have a much better appreciations for olive wood, here's what I plan to do if I ever get a chance to go back:
1. Try to make contact with other IAP members in Israel and see if they might be able to help me find some good sources of olive wood. (use the advanced member search to find members in Israel - it looks like we have 14 members, but only a couple of them are currently active).
2. Do some research and try to find olive wood sources in whatever part of the country you will be spending the most time. I didn't do any prior research last time and we were quite busy most of the time, so my colleagues didn't really have time to help me hunt for wood. If I had asked them about it a few weeks before my trip, they could probably have helped me out more.
3. Bethlehemolivewood.net has already been suggested & they are located in Jerusalem. I would definitely check them out & see if I can visit. Another possible source in Jerusalem is ebay seller olivewood2000 - I have purchased a number of pen blanks from him and have always gotten good quality. He is in Jerusalem also. Getting around in Jerusalem is no problem. I had a rental car and drove all over the country by myself, but I did not attempt to drive in the West Bank alone. I would not recommend that - either use a tour bus or a personal guide like I did if you want to go into any West Bank areas. A personal guide is certainly more expensive, but you can go where you want on your own schedule and see & do a lot more.
4. Pack light or just take older clothes on the trip & throw some of it away to make room for wood. Buy as much olive wood as you can and pack your suitcases up to the weight limit. Sure, buy some pen blanks, but get as much larger wood as you can, especially some with bark for natural edge projects. You will probably need to visit the shops of some carvers like I did to get that kind of choice wood. If you can, try to arrange such visits in advance - I really lucked into the opportunities I had. Prior planning would have been much better, but at the time, I had no knowledge of wood turning whatsoever.
Hope this helps - enjoy your trip.
Edgar