Hi GrendelsMum..
I've been to Syria a couple of times out of Dubai where I live, I'm British but my DH is Jordanian and he would say take an organised tour unless you can speak Arabic or are very good at not being ripped off!
I think Syria is a country where any western tourists are seen as being wealthy (and we are compared to them) and they see no reason why they shouldn't try and squeeze as much out of you as possible, so hotels will always be a bit more expensive etc. You need to have your wits about you.
That said, it's a very beautiful country, we've stayed in Damascus which has had a good stab at making the old city quaint and traditional - stay in a boutique hotel in the Old City if budget allows, they are converted Damscene houses set around a courtyard and absolutely gorgeous, we've stayed in Old Vine Hotel and Dar Al Noor (google for websites) and really haggle them on prices. We travelled to Palmyra (Tadmor) to see the ruins in the desert, Hama for the Norias (water wheels), Crak De Chevaliers is an absolute must and you can do it in a day trip from Hama, Aleppo is also a fantastic place and probably more enjoyable than Damascus (not as much traffic, nicer souks).
Overall it's a friendly Middle Eastern country, has lots of Med influence (try Latakia on the west coast), it's also very unwesternised (eg; no Mcdonalds/Pizza Hut thank goodness!)
Because we can speak Arabic, we've managed to travel around by coach, I wouldn't advise hiring a car - the driving is horrendous, I've always seen tour parties where we've been, you can probably manage Damascus alone and then arrange tours to the other towns/sites.
There's lots of friendly information on Tripadvisor, but ask if there's anything you specifically want to know.