参考答案：

Dear Mr．Smith，

I am really excited about the stay in your family last week．I want to express my most sincere appreciation for your hospitality.

I had a really agreeable dinner with your amiable family. I quite enjoyed myself with your warmth and generosity. It was nice of you to introduce me to so many natural scenes in Beijing.

Meanwhile, I hope you will someday pay a short visit to my hometown, Shanghai. I will be very happy to be your guide and show you around. I look forward to your reply.

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Yours sincerely,

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 Li Ming