Could you help with a letter to a friend,please

Here is the letter.

Dear Jan
1) I hope you are all well, and that you’ve recovered from the busy Christmas period.
2) I’m writing to ask you a favor. 3) I’m coming down to London at the end of the month to go to a conference. 4) It’s the 22nd – 24th January. 5) Could you put me up for a few days? 6) I don’t mind where you put me. 7) I’ll sleep anywhere!
8) There is something else I’d like to ask you. 9) Could I have a bite to eat when I arrive? 10) Just a sandwich will do. 11) I hope that’s all right.
Write soon and let me know.
Best wishes
Chris

I'm not quite sure about the right order of the sentences, especially with the number 2. At first I put it in the beginning of the letter but then I thought that starting your letter with a direct request is not very nice. Am I mistaken here?
Thanks for your help!