Asoko de nanika nomimasen ka

I have already asked this question before but what I didn't understand in the response is that :
Till now I have studied that de particle is used when an action takes place at a particular place.
But in the conversation the person is asking someone shall we go there to drink something or would you like to go there to drink something.
The action is not been performed yet in that place so why is de particle coming with asoko de. Pls. Clarify this doubt of mine ASAP.

「But in the conversation the person is asking someone shall we go there to drink something or would you like to go there to drink something.」

That's actually not what they're asking.

「Asoko de nanika nomimasen ka」 literally translates to "Won't you drink something there?", or more naturally translates as "Why don't we have a drink there?" or "Shall we have a drink there?"

There's no use of "go" ("iku") in the sentence, so "de" is connecting to the verb "nomimasen/nomu," which means "drink." "Asoko" is the place where the action of drinking will be done, so "de" is the correct particle.

"Shall we go there to drink something?" would be "Asoko ni nanika wo nomi ni ikimasen ka?" In that case, "there" is connected to the verb "go" as the target of motion, so the particle to use would be "ni."

de particle is used when an action takes place at a particular place

You've misinterpreted the "when". It doesn't mean that the action has to be taking place "right now". It's something like the English word "at".

I am drinking something "at" the cafe.
Would you like to drink something "at" the cafe?
I had something to drink "at" the cafe.

They all work.