Dear host family,
First of all we would like to thank you for giving our daughter () the chance to become an exchange student and a part of your family for a few months.
() was born in () on (). She attends the ninth grade of a “Gymnasium”. We still live in (), a town in Westphalia with more than () inhabitants. We are a small family, () is our only child, but we live together in a big house with ()’s uncle, aunt, cousin and grandmother.
Last autumn, when () returned from a class trip to Whitstable, she was so enthusiastic that she asked us to allow a longer stay in a foreign country. She likes England very much: the towns, the countryside and also living in an English family. After a short time of thinking we agreed, because we are convinced that a stay in a foreign country will make young people more adult and self-confident. Besides it is a great chance to improve her English.
Self-confident – that is the keyword for the description of our daughter: At home in our family () is very self-confident, but together with other people she often is little bit shy. So we request you to be patient with her. After a few days in your family () will “unfreeze” (how we say in Germany).
Music is another keyword for the life of (): Since seven years she plays piano. And in February she began to play viola. From her 7th to her 13th age she was member of a Children’s Choir.
() is responsible, honest and does very well at school. We never had problems with her. Only her room sometimes looks a little bit like a battlefield…
We thank you for taking the time to read our letter.
Kind regards!
Danke für eure Hilfe!
Also, ich denke, Geburtsdatum kann man weglassen, das steht ja sicher noch woanders.
Statt „Westphalia“ würde ich „Western Germany“ schreiben, weil sich eine Gastfamilie sicher nicht vorstellen kann, wo das liegt. Hier würde sich auch anbieten zu sagen: Stadt-x liegt ca. x Kilometer von… eine grosse Stadt in der Nähe.
Das mit der Musik würde ich etwas ausformulieren, z.B., sie liebt es, Viola zu spielen, übt jeden Tag usw.
Dann würde ich noch was über die „geplanten Hobbies“ reinschreiben, also was Ihre Tochter gerne machen würde im Ausland.
Waren nur so ein paar Vorschläge 
LG
Hey,
ich hab mal den Brief korrigiert und umgeschrieben. Ich würde noch mehr über deine Hobbies schreiben (oder spielst du wirklich nur Musik in deiner Freizeit ?).
Dear host family,
first of all we would like to thank you for giving our daughter () the chance to become an exchange student and a part of your family for a few months.
() was born in () on (). We now live in (), a town in Western Germany with more than () inhabitants, in a big house together with ()’s uncle, aunt, cousin and grandmother.
Currently () attends 9th grade at high school. Last autumn () spend a week (?) in Whitstable with her class and just loved it. This is why she got the idea to become an exchange student. She is pretty fascinated by England - both the towns and the countryside and also daily life of a British family. We are convinced that a high school year will help her to become more independent and self-confident. Besides this it also is a great opportunity to improve her English.
() is open-minded and pretty talkative but when meeting new people she often is a bit shy at first.
Music is her passion - she has been playing the piano for about seven years now and has recently started to play the violin. Furthermore as a child she attented a choir .
() is responsible, honest and does pretty well at school but is a bit chaotic from time to time …
Finally, we`d like to thank you for taking the time to read our letter. We would be glad if () could spend her high school year with you guys !
Kind regards,
(…)
Viele Grüße,
Marie-Claire