elves - How old was Lady Arwen, wife of Aragorn in the Lord of the Rings?

We know this exactly since the appendixes contain birthdates for many characters. Arwen was born in TA (Third Age) 241, Aragorn in TA 2931.

So Arwen was indeed 2680 years older than her husband.

Considering the age difference , would not Aragorn seem to be a small kid in front of her ?

You cannot simply compare age differences the way we humans do among each other. The point is that Aragorn was himself over 80 years old, had travelled extensively across Middle-Earth and survived many adventures, gaining as much experience and wisdom as a human could. Additionally, he was of the royal line of Numenor, so he had some Elven ancestry himself (indeed, Arwen's father is Aragorn's Great-great-<many, many, greats>-Uncle) and inherited some of the innate Elvish nobility along with a greater lifespan.

Even to an immortal Elf who's thousands of years old, someone like that is not in any way a child. Also note that while the Elves themselves take longer than humans to reach maturity (between 50 and 100 years), Aragorn would have been considered a (young) adult by their standards as well.