• Turkey is only safer than actual Daesh-held territory - Turkey has a long history of ethnic cleansing and persecution of minorities, and is actively scuppering the attempts to fight Daesh of its own Kurdish population, and occasionally outright attacking them itself. It's relatively easy to pass through, but not a good place to stay for anyone that isn't the Muslim Turkish majority.
• Lebanon, as good as it may be, is one nasty push from being the front-lines of Daesh.
• Jordan has already taken in far more refugees than any country can be reasonably expected to take in - there's around one refugee in Jordan for every four Jordanian citizens.
• Israel, as always, is itself contributing the numbers of refugees, slightly, and are openly hostile to any Muslims there.
• Palestine isn't in a fit condition to help its own people, never mind refugees.
• Iran has taken in just over 30k refugees from Iraq. However, due to Sunni/Shia friction in the area, many Sunni (the majority of Syria and Iraq) refugees opt not to go there. On top of that, travelling to Iran would mean actually crossing through Daesh-held territory in order to get there. • Kuwait has an absolutely tiny habitable area, and couldn't really support any kind of large refugee population. On top of that, again, travelling to Kuwait would mean crossing Daesh-held territory. • Travelling to the Gulf states (UAE, Bahrain, Qatar, etc.) actually means crossing thousands of miles of desert on foot, which would be hard for even the well-prepared to do.
• Saudi Arabia is one of the strong candidates criticism, as they're in the vicinity, have (relatively) nearby habitable area, and have the surplus resources to keep a refugee population. However: 1) The government of Saudi Arabia is a selfish, greedy, totalitarian despotic monarchy, and 2) Even if they did offer refuge, a number of the refugees may see the Saudi government as not being that too much more preferable than Daesh.
• Egypt has taken in a decent number of refugees (>130k), but the refugees there aren't exactly in the best of conditions, and a lot are crossing the med to get to Europe.
• The caucasus states collectively have taken in a huge number of refugees - Armenia at >100k, Azerbaijan (the Turkic, Shia Caucasian state) at >300k, and Georgia at >500k. It should be noted that, while Azerbaijan is culturally Turkic like Turkey, and Shia like Iran, it's also secular and far separated from the Sunni/Shia ethnic tensions of Iraq, so religion isn't as much of a problem.

TL;DR: If you want to break out the pitchforks at anyone besides Daesh, go after the Saudi government and Turkish governments, who have been exacerbating the problem.