Thanks to a slight glitch in a computer system, DW, DD and I are headed over in Feb. We'll have 4 full days on the ground. We are planning on a day in Old Jerusalem, a day to Masada, haifa and a day to fill in any gaps as we go along.
If you only have 4 days - stay in Jerusalem. There is enough there, in the old city, to keep you entertained for a lot more than 4 days. Christian sites, Jewish sites, Muslim sites (Dome of the Rock). 2000 old archeology and restored buildings. The old market. The original Hell (
Gehenna). And a lot more. Just wander the streets of the old city, they have a very special feeling.
Remember - there is nothing in the world like Jerusalem - it even has its own mental illness.
Masada's story is heroic but on the ground all you see are some crumbling stones. The night show is interesting but the hours you'll spend on the drive are not worth it. Haifa has great views and the Baha'i gardens but it does not compare to the atmosphere in Jerusalem.
I recommend leaving the US on a Friday or Saturday so you will not have ultra-religious Jews praying in the airplane and disturbing you. Arriving on the Saturday (Sabbath) you will avoid most of the hassle of the weekend in Jerusalem. Muslems on Friday and Jews on Saturday are a thing to avoid, also a lot of places are closed on Saturday. Note that Sunday morning and Thursday afternoon are times of very heavy traffic, more than usual commuting, if you want to get anywhere.
If you are female - carry a couple of large pieces of cloth (shawls, scarves) to cover yourself in Holy sites. Mostly people will not say anything but you may feel uncomfortable if not covered. That is more relevant in summer when people wear shorts and tank-tops.
Another advice - in other countries they tell you not to look like an American tourist. In Israel that is EXACTLY what you want to look like. You don't want either side (Jewish or Muslim) to stone you, so try to look rich and Christian (even if you are neither). If people think they can get your money (and your political support), they will treat you better.
For the OP - July in Israel is deadly, and I mean it literally. 35 degrees Celsius (almost 100 deg Fahrenheit) and breath taking humidity. The only thing you can do is prostrate yourself on some beach until you are crispy. Do not even think about Masada in July, unless it is a night-time tour of the desert around it, which is quite interesting.
The best time to visit is March-April or October-November but February is OK. August is slightly better than July but not by much. There is no point in spending a lot of money and then just staying in the hotel because you cant walk and breath at the same time. In any case, for 11 days I recommend Sunday to Friday morning in Jerusalem and the rest of the time in Haifa with a day trip from Haifa to Acre and another to Zafed/Tiberias. You don't need a tour company, just take a regular bus.
Weekends - the weekend is Friday-Saturday and most places are closed from Friday noon. Haifa is good on the weekend - they even have buses, Jerusalem is dead on the weekend, check other sites carefully about that.
Masada's moto is "Masada shall not fall again", I prefer - he who fights and runs away, lives to fight another day.