I looked everywhere I could where I think I lost it, but I couldn't find it.
I searched for it where I think I may have dropped it, but it didn't turn up anywhere.
この場合、次のような言い方ができますよ。
ーI looked everywhere I could where I think I lost it, but I couldn't find it.
「無くした思うところは全部探したけど、見つからなかった」
to look everywhere で「方々探す・探し回る」
where I think I lost it で「それを無くしたと思う場所」
ーI searched for it where I think I may have dropped it, but it didn't turn up anywhere.
「落としたかもしれない場所を探したが、出てこなかった」
where I think I may have dropped it で「落としたかもしれない場所」
to turn up で「発見する・見つける」
ご参考まで!