Learn English – “Live in the moment” vs “Live for the moment”

I wouldn't say that the phrase What is for? is completely ungrammatical. Phonetically, it sounds like you're literally asking what does the word for mean:

What is "for"? (What does it mean and how to use it?)

What for? is, of course, the idiom you should use in this situation because it's a legitimate expression in English and it means exactly what you intend to say:

for what purpose? why?

Example:

— Tomorrow, I'm going to my Mom's. Will you come with me?
— What for?
— Well, you could help her in her garden.

Although a period of time can be called "an age", as in the stone age, in the context you give "age" seems more specifically like you are talking about the individual ages of people.

If you are trying to say that an item or a thing is appealing to people of all different ages or age-groups then I would prefer something like:

Suitable for all ages.

But if you are trying to say that something will last for a long time or appeal to people of future generations then I would personally use the word "timeless" or "enduring". Your suggestion of "for all times" is not a recognisable phrase and rather ambiguous.

You could say:

This has timeless value.

or

This has enduring appeal.