you can say we will go shopping. or we will go to the shops.

Hi... "We will go shopping" is the correct sentence.

we will go shopping is the bast choice it sounds natural, most grammatical n native go shopping is a fix structure like go swimming, go skiing, .... but we cannot say go to swimming or go for swimming, .....

you can say we will go for shopping ,we will go to shop or we will go shopping.i think we will go shopping is the most people use

"We will go for some shopping" is correct too. "We will go to shop".