My favorite city in Tokyo

My Favorite City in Tokyo

Fixed capitalization for the title

My favorite city in Tokyo is Daikanyama.

Removed the period because this should be part of the next sentence

because there are so many interesting places: restaurants, fashion stores, bookstores, and so on.

英語の文にたいして、接続詞("and", "but", "or", "because", etc.)を最初にしない方がいいです。それから、前の文と接続しています。
English sentences shouldn't start with conjunctions. Therefore, I'm combining this with the previous sentence.

I like to look into just browse that those stores without purpose.

「browse」は使いたがっている動詞です。「just browse」は理由もなく、見ることだけをするという意味です。

Sometimes I bought buy something, but mostly I bought don't buy nothing anything and just looking.

過去にしたことですけど、こいう説明で今的でいえるとはもっと自然です。
It may have happened in the past, however this kind of explanation sounds most natural in the present tense.

Daikanyama is more quieter than Shibuya or Ikebukuro and so on, so which is why I love it.

所の名は頭文字を使います(例: × "tokyo" ○ "Tokyo")。〜erか〜estを付けれる形容詞にたいして、「more」と「most」は使えません。
Place names start with capital letters. Adjectives that can use the -er and -est endings can't use "more" or "most".

I don't like noisy, croweded places..

Minor spelling fix ("crowded"), deleted an extra period.