See you: Görüşürüz , Görüşmek üzere.
Take care yourself: Kendine iyi bak.
Have a nice day : iyi günler.
Goodbye====
If you wanna use Goodbye in Turkish, u can use "güle güle", "hoşçakal", "Allah'a ısmarladık".
But there r some diferences.
hoşçakal : Hoşçakal is said to the person who stays by the person who is leaving. (first situation)
güle güle: It is opposite of Hoşçakal. (second situation)
Allah'a ısmarladık: it can be used in both situations.
Formal using: Hoşça kalın (first situation). Güle güle (second situation)
Informal using: Hoşça kal (first situation). Güle güle is also for informal using (second situation).
We usually use "iyi günler/akşamlar/geceler for formal using more. Also u can use these for informal too. Already there isnt a sharp border between formal and informal in Turkish except for a few things. When u use words as plural they r converted to formal.
But if u r seeking best word, it is "selamun aleyküm" for hello and goodbye. it means "peace be upon you" or "Allah's selam be upon you". This is muslim word. So it is used in all muslim countries.
selamun aleyküm :)