In chapter 21, Anne Moody states that the Tougaloo chapter of the NAACP organized a demonstration at the state fair in Jackson. Anne didn't go but watched the demonstration take place on TV at her student dorm with the other female students. When Dave Jones was interviewed, she states that it was the first time that someone from the NAACP had appeared on TV.

When the police returned the students to their student dorms in their cars later that night, it brought great excitement to everyone involved. Soon they were organizing more demonstrations and boycotts. On page 296, Moody and her friends join Reverend King to demonstrate outside a post office in Jackson with the idea that police couldn't arrest them because the post office was federal property.

On page 288, Moody talks about a sit-in at Woolworths on Capitol Street in Jackson. To divert attention away from the sit-in, Moody states that some people started picketing J. C. Penney's.

There are at least a couple of different ways that you could answer this question, depending on what exactly you mean by "where."

If you are asking what city or town the demonstrations take place in, then the answer is that they take place in Jackson, Mississippi.  Anne has gone to Jackson to study at Tougaloo College there.  While there, she becomes more and more involved with civil rights until she finally participates in the NAACP's program of demonstrations and sit-ins.

If you are asking where in the town of Jackson the demonstrations take place, there are many of them.  The first demonstration takes place in front of a J. C. Penney store.  While the picketers are protesting there (and getting arrested) Anne and her friends slip into the Woolworths store.  That is where they conduct their sit in.  Later demonstrations took place all over the downtown area of the city.