I have something else I need to do next week, so let's settle on a date soon.
I have other plans next week, so I'd like to pick a day for us to get together as soon as we can.
この場合、次のような言い方ができますよ。
ーI have something else I need to do next week, so let's settle on a date soon.
「来週他にも用事があるから、早めに日にち決めよ」
to settle on a date で「日にちを決める」
ーI have other plans next week, so I'd like to pick a day for us to get together as soon as we can.
「来週他にも予定があるから、できるだけ早く遊び日を選びたい」
to pick a day「日を選ぶ」
他の予定が1つだけだとしても、to have other plans と複数形とします。
ご参考まで!