It will be warm in July, so that's good for packing light! I would keep clothes to a minimum, and bring things that dry fast so you can wash them out in the hotel sink and they're good to go in the morning. (Jeans are a nightmare to wash on the go...) Remember that you can buy most anything you'd need in Italy or Israel, so no need to bring a lot of extras just in case.
I would bring 1 pair of comfortable black pants that could pass as dressy for a nice restaurant or concert (I have some from Patagonia that I love)
1 pair of hiking/travel pants or capris
1 pair of shorts
for working outside you'll likely want a grubby t-shirt and shorts which you can throw away when you're done!
something to sleep in (nighty, shorts, etc. if you're staying in hostels remember you might be seen in it...)
1 skirt and/or dress (if you are a skirt/dress king of person, otherwise maybe another pair of shorts)
2 tank tops
2 t-shirts
1 or 2 long-sleeved shirts for when you need to be modest (such as religious sites in Israel)
a light fleece/jacket for cool evenings
a pair of versatile sandals (Chaco's are great)
a pair of comfortable walking/hiking shoes
a few pairs of socks (I like Smartwool ones and they dry fast and don't stink if you wear them for 2 days)
2 bras and 5 or 6 pairs of underwear
swimsuit
a sarong or scarf (or just buy one, Israel has lovely ones for cheap)
a sun hat
sunglasses
sunscreen
travel size toiletries (you can easily buy more in the countries on your itinerary)
a small container of laundry soap (shampoo works fine too)
camera/charger (you'll need an adapter but you can buy one over there for a few dollars)
whatever other electronics you use, such as netbook/ipad/ipod, etc.
journal
guidebook
a few books to read or better yet an e-reader
if you're staying in hostels, it can be nice to have a sleeping bag liner in case the cleanliness is not so good
earplugs/eye mask for sleeping in less than idea conditions
a travel wallet with passport, ATM card, credit card, ID
photocopy of passport, backup ATM card, and a few hundred dollars (or other currency) of emergency money kept separate from the wallet
I like to use a smallish backpacking backpack, like around 40-50 liter size, and also a small handbag for valuables.
Well I'm sure I'm leaving some important things out, but that is my suggestion off the top of my head. Remember to leave room in your bag to buy things along the way. Sounds like a fun trip!
