Breakdown of Я иду в столовую.
я
I
в
in / to (direction)
идти
to go (on foot) / to proceed, go (of a process)
столовая
canteen, dining hall
Questions & Answers about Я иду в столовую.
Why does the word for canteen end in "-ую" here?
It is in the Accusative case because it is the destination of your movement. The dictionary form is столовая. Even though it is a noun, it has a feminine adjective ending (-ая). Therefore, it changes to -ую in the Accusative case, exactly like a feminine adjective would.
Why do we use the preposition в instead of на for the canteen?
We use в (meaning "into" or "to") because a canteen is a physical room or enclosed building. You typically use на when going to open spaces (like a street) or events (like a concert or lesson).
Could I use хожу instead of иду if I mean "I go to the canteen"?
Not if you mean you are on your way there right now. иду means you are walking there at this very moment in one direction. You would use хожу if you were talking about a repeated habit, like going to the canteen every day.
What question word would prompt the answer в столовую?
You would use куда, which means "where to" or "to what destination." For example, Куда ты идёшь? (Where are you going?). You would not use где (where at), because где is only used for a static location, not a direction of movement.