I know I'm rather late in replying to this thread, probably too late to help you, but maybe this will help others:
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It is quite easy to get to Qalaat Najm on your own. I've done it a couple of times. There are two options from Aleppo: take a microbus bound for Ras al-Ain and ask to be dropped at the turn-off for Qalaat Najm. Wait there for a microbus to the village before the castle. Or take a microbus from Aleppo to Manbij and catch the same microbus to Qalaat Najm from there. Locals in Manbij are pretty helpful and will get you on the right microbus. Sometimes the driver will take you all the way to the castle, other times he won't go further than the village about 2km before it (but it's a nice walk the rest of the way). To get the return microbus, you'll have to walk back into the village. I'd make sure to start your return by 4PM.
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There is a mosque built on the slope of Jebel Qassioun which claims to be built over the cave of Cain and Abel, but I don't think any of these locations are really known. Either way, you can hike there from Salahiyeh (or Sheikh Muhaddin as it is often referred to).
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Last time I was in Deir al-Zur, Abu Kamal was strictly off-limits to foreigners. I don't think that has changed. Syrian authorities believe the only people interested in such a place would be journalists and/or spies, so... you'd be better off avoiding it. And by all accounts I've heard from some Syrian friends from Deir, there is nothing there to see. (Though there are apparently some ruins about 1km from the border on the northeast side of the Euphrates, I'd have to assume you'd be arrested before being allowed there.)
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As far as I know, yes. I haven't been.
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There are a couple budget hotels in al-Raqqa near the center of town. Not very inspiring, but there is hot water. I've heard there are two budget hotels in al-Suweida, but I haven't stayed in either. Daraa has a couple options, too. Hassakeh has a bunch of hotels, no problems there. Idleb has some mid-range hotels, but I'm not sure about budget options. Ariha and Maarat al-Numan I don't believe have any accommodations, but I could be wrong. In the Idleb/Maarat al-Numan/Ariha region I've never had trouble getting invited to stay at people's homes. It is a nice way to experience that area. Same with the dead cities region west/northwest of Aleppo (around Sarmada, Harem, etc. or the Kurdish areas around Barad, Burj Haider, etc.).
