My hobbies are things like traveling and cooking... I have many!
I have several hobbies like traveling and cooking!
My hobbies include traveling and cooking... among other things!
「趣味は旅行とか料理とか…色々だよ!」という文章を英語で表すと、この三つの文章と使っても良いと考えました:
「My hobbies are things like traveling and cooking... I have many!」
「I have several hobbies like traveling and cooking!」
「My hobbies include traveling and cooking... among other things!」
「趣味」は「hobbies」という言葉になって、「旅行と料理」は「traveling and cooking」になります。「Include」という言葉は「含める」という意味があります。
I like travelling and cooking in my free time as well as many other things.
この場合、次のような言い方ができますよ。
ーI like travelling and cooking in my free time as well as many other things.
「趣味は旅行と料理、それ以外にもいろいろです」
as well as many other things と言うことで、そのほかにもたくさんあるという意味になりますよ。
ご参考まで!