"It was when he reached the bottom step that it occurred to him how very pleasant it would be to pass the vegetable patch on his walk to Hagrid's."
The vegetable patch on the Hogwarts Grounds is located near the greenhouses. The food grown there is used in the food served at Hogwarts.
The main reference to the vegetable patch is when Harry, using Felix Felicis, encounters Professor Slughorn as he was on his way to Hagrid's (HBP22). Professor Slughorn had just collected leafy plants for his third years with permission from Professor Sprout.
J.K. Rowling references the vegetable patch that is near the greenhouses many times in the series, but she also mentions another one. In CS7, the narrator explains, "In the small vegetable patch behind Hagrid's house were a dozen of the largest pumpkins Harry had ever seen." We can assume this is not the same vegetable patch because students have to cross the vegetable patches to get to the greenhouses, and it would not make sense for the students to cross behind Hagrid's house.
Throughout all of the smaller canon references (above), J.K. Rowling switches between singular and plural when referencing the vegetable patch(es).