Can I put in a vote for Tarah! ? This is widely used in the north of England as a friendly alternative to the more formal 'Goodbye'.

When I was growing up in the north, the informal version of 'Hello' was 'Iya' - that's Hi ya with the 'h' missing  - (never just 'Hi'), and the informal version of 'Goodbye' was 'Tarah'.

I remember, when I was a teenager, I met a girl from London on a coach heading south, and I noticed that she said 'See you' to me when she got off the coach. That's strange, thought I - I'm fairly sure that she'll never see me again. That was the first time I'd ever heard anyone say 'See you'.

"Later" only one word. Easy and quick, good for friends 

"Peace out" or "peace" kind of silly but I say it, mostly men say this i think 

"See ya" basically same as see you later 

 I just want to add 

" later! " and " so long ". 

Sudeep, you are right that 'ta-ra' and 'ta-ta' are related. I think that 'ta-ra' is probably just a regional variation on 'ta-ta', but we don't necessarily wave when we say it. 'Ta-ta' is more widespread, and has been around since Victorian times, so it is not surprising that the British imported it to India. 'Ta-ta' is  mainly used when speaking to small children, which is why there is a hand-waving gesture connected with it. It's a way of teaching babies to associate leave-taking with a hand wave and the simple repeated syllables.

Leyla, (or anyone else who's interested). If you wants to hear an old rock and roll song called See You Later Alligator, just search for it on youtube. The most famous version was recorded by Bill Haley and His Comets in 1956.

informally and idiomatically, we say  "GOTTA RUN"  

in very formal meetings,  we say "LET'S CALL IT A DAY"

in carefully caring for someone, we  say "TAKE IT EASY" or "STAY WELL"