"spend the day" is correct and usable in written English. It is typically used to indicate that someone will use or pass the entire day engaged in a certain activity or location. Here is one example of its usage: "I can't wait to spend the day at the beach tomorrow. It will be so relaxing to just lay in the sun and listen to the waves."
They spend the day together.
I spend the day smelling flowers.
I spend the day in fruitless search.
You could easily spend the day here.
We swan off to spend the day out walking.
It's a fun way to spend the day".
Sojo will spend the day with his children.
Most of the teachers spend the day reading the newspaper.
On Friday, she and Maia would spend the day together.
Spend the day doing radio interviews in my pyjamas.
"In practice, you spend the day meeting, selling.
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia