My son hunted up and down exploring various places, while my daughter found some flowers.
It was a day off with warm weather so I let my children play outside for the first time in a while.
「男の子はあちこち探索して、そして女の子は花を見つけました」 ＝＞
"My son hunted up and down exploring various places, while my daughter found some flowers."
探索する ＝ explore, search, hunt
あちこち ＝ here and there; up and down
various places = いろんなところ（で）
"It was a day off with warm weather so I let my children play outside for the first time in a while." ＝＞
「休みの日が暖かかったので久しぶりに外で遊ばせた」
アメリカ合衆国 
