Just need some help writing

Hello, I want to write a letter and I want it to say.

I go to school at Arizona State University and my major is cultural anthropology. I can't wait to meet you in person, thank you for taking me in your home.

perhaps a fluent speaker can help later but here's what i can do.

I go to school at Arizona State University and my major is cultural anthropology. I can't wait to meet you in person, thank you for taking me in your home.

私はアリゾナ州大学で勉強しています。専攻は文化人類学です。会うときを楽しんでいますよ。御
宅に誘ってくれてありがとうございました。

わたしは　アリゾナしゅう　だいがくで　べんきょう　しています。せんこうは　ぶんかじん　るいがくです。あう　ときを　たのしんでいますよ。おたくに　さそって　くれて　ありがとう　ございました。

That last sentence I'm not so sure about.

The "I can't wait to meet you in person" sentence should be:
(In kanji and hiragana) 会うのを楽しみにしています。or 会えるのを楽しみにしています。
(In hiragana only) あうのを　たのしみに　しています。 or あえるのを　たのしみに　しています。
(In romaji) "Au no wo tanoshimi ni shite imasu." or "Aeru no wo tanoshimi ni shite imasu."

(To Miyuki: "tanoshinde imasu" is "am enjoying." To say "I look forward to...," you would want to say: "tanoshimi ni shiteimasu.")

The last part "Thank you for taking me in your home": do you mean it as "thank you for accepting me to stay at your home," like for an exchange program, or maybe it's some e-mail friend/penpal of yours who agreed to put you up during your stay in Japan?