si lo que quieres es decir que vas a pasar el día viendo tiendas de ropa, zapaterías, complementos, etc... por ejemplo en un centro comercial, tendrías que decir "voy de compras" si lo que quieres es comprar comida, cosas para la casa, etc... dirías "voy a hacer la compra"

"I go shopping" es más generalizado. podría referirse a cualquier clase de las compras. "grocery shopping" se refiere a comprar comida sólo. "groceries" son comida. Lo siento, mi español es malo

Hago is from the base word hacer.....yes, I know that you know that :-) Anyway, hacer= to do or to make. So, you can say (at least here in the US).....I do the shopping. I'm going to go to the grocery store. I'm going to go to the store. Grocery store is more specific because "store" could mean: hardware store or chicken food supply store or any kind of store you can imagine. Some people even say: I'm going to the super market. Some people say: I'm going to do groceries. LIke...for example ....I'm going to do the laundry now. Maybe I gave you more information than you wanted. Sorry it was so wordy. :-)