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For example, let's say someone says
いつでもいいよ！
In English I would just simply say, "okay, sure, alright" just to tell the speaker I heard what they said.
I initially thought to reply with はい but that doesn't feel right, it feels like はい is more of a confirmation than simple acknowledgement.
Is はい the proper term to use to acknowledge this kind of statement? What other ways can I acknowledge someone said something?
「はい」 would not be an improper or unnatural reply for that at all. Of course, it might sound more natural if you elongated the first syllable and said 「はーい」.
Unlike what bilingual dictionaries might say, 「はい」 does not always mean "yes". Instead, it is very often used to mean "Sure, I heard ya", and when it is used for that meaning, the person saying 「はい」 may not be in agreement with the other person at all.
Other phrase choices would include:
・「わかった」
・「オッケー」
・「ほーい」
・「了解{りょうかい}」
・「よーし」
・「よっしゃ」 ← slightly dialectal
I think it depends on the context. Let's say if you are talking about a meeting with him/her, and you asked "When should we meet?"
She says "itudemo ii yo!"
Then you might say, "ok! ato de renraku suru yo"
This means "ok 後で連絡するよ！"
