You can say "see you" over the phone! I would use "see you" more than "see you later" because "see you later" is saying that you will see them later that day. Even though it is a phone call and you didn't "see" them, in English we still say "see you" and "see you later"! I hope this was helpful, Ava

You can say...it was nice to talking to you...then hang up

Yes, you can use "see you" over the phone! However, save this for people you know a little bit. If you're not sure, a standard "goodbye" is perfectly fine.

"Goodbye" is always polite and always friendly. Don't feel you need to use anything else. In English, we often use the word "see" figuratively to mean "meet" or "have social contact with." I never even thought about how strange it is to use in a telephone conversation. There are other such peculiarities. As for whether to use "see you," a native English speaker picks up cues from the other speaker and matches their level of formality and their turns of phrase. In closing a conversation, it is common to echo what the other speaker says. English speakers use many different phrases to close a telephone conversation. Any phrase that can be used in person is also used on the phone. "Bye," "Bye-bye," "So long," "See you," a few friends of mine even say "Ciao."