Any Americans spent much time in Syria? How were you received? Can anyone recommend a small-group tour operator? Is there any really nice place to spend more time after a tour? Thanks!

Totally safe...I just went there for a month. The people were great, friendly, and more hospitable than I could have ever imagined. There was no hostility presented towards me for being an American. None. People will ask you about your politics tho. Be prepared to answer questions about Gaza, the Iraqi shoe thrower (at Bush), and Obama. Gaza is a big deal, so I would not suggest trying to defend Israel.
The country is safe. You can walk the streets late at night and there is no problem. At least I had none.
I did not know a lick of Arabic. I would suggest knowing the word shukran (thank you) and fursa saida [sieeda] (nice to meet you). Talk to people when you are traveling on the train or bus. There is a good chance they will take you back to there home to stay. 2 out of 2 times this happened for me.
Security will hassle you at the train station or taxi stand (for long distances...I crossed to Lebanon from Lattakia and they wanted to know what I was up to). Make sure you get a taxi with a meter and that he turns it on.
People are great. So friendly. I can't tell you enough...
Have fun
I just wandered around myself, btw. I rented an apartment in the old city in Damascus for a month for $300, which I think is more than I should have paid... I think there is a place you can look up called yallahhouse...check it out. You can live in a house for cheap. Way better than a hotel. No hostels are there.
Syria is very easy to do alone. Even when you remove the perceived "safety" that many people attribute to tours--totally unnecessary in Syria-- the distances are not great. It's quite easily covered by public transport.
I'm American, but I'm also Asian so my experiences are different. But I always said I was American when asked, and often people responded, "I love Americans!"
My favorite Arabic phrase is "mafi mushkala." No problem!

just came back a couple weeks ago I traveld independantly no problems whatsoever all you need is an LP syria lebanon book should answer all your questions If you want to do tours hotels can arrange them or there is always a taxi you can hire for the day or half day as you chose.
As with being an American I am too People will ask where you are from tell them YOU are an ambassador of our country over there leave them with a good impression 99% of people when I said I was an American will say welcome to Syria. The Syrian people have no problem with us it's our goverment.
enjoy it is not crowded this time of year and a great time to go