Recommendations for the Must Eats of Beijing and Chiang Mai?

My hubby and I will shortly be abandoning our pug into my brother's care and boarding a plane for Asia. Our plan is a week in Beijing and then another few weeks in Thailand. Justin's hope is to eat his way through Asia. This is why I love him. We have basically the same travel goals.

We are also looking for a great, mid-range place to stay in Beijing near Tienaman Square. Anyone have a recommendation? The plan, after seeing the forbidden city, etc is to seek out Peking duck, dumplings, and anything else that looks delicious. I was in China 12 years ago. I have a feeling a great deal will have changed. I am excited to see the city, but I hope the pollution won't be too bad.

Once we get to Thailand we will be headed to Chiang Mai for cooking school. I have a few picked out, but has any reader had a good experience with a particular school. I don't really want the basics, but something a bit more advanced. Then off to an island for some swimming and fun. We will fly out of Bangkok, so we will have a few days there to see the city and all it's sites.
I am so excited to be traveling abroad again. I am already packed, immunized, and prepared for whatever adventure comes our way!

Most importantly, any recommendations for must eats, must visits, or must see while we are there? I am pretty sure that I won't be posting while traveling, but check back in August for some Thai dishes. :)