Chedi Phra Pathom is a sacred place, which, because of its proximity to Bangkok, is often visited by people from Bangkok. Chedi Phra Pathom is somewhere that you go with your family.
I've been there several times and each time I admire the Thais who give gifts and prayers to the statue of the Buddha, opposite the staircase of the main entrance. Fewer people go to the tower of the Chedi. Although as it has a circumference of 235m there's plenty of space to avoid walking into other people.
Chedi Phra Pathom is made up of several buildings that are part of the strcuture that surrounds the main dome. They include a meditation room, an ordination room and Vihara (monasteries) at each cardinal point, one of which has a reclining buddha, and another amazing frescoes on the walls. Sometimes you will meet apprentice monks.
There are also some interesting narrow cavities which can contain statues or a place to pray. I smiled when I saw a man who was supposed to be praying, sleeping quietly on 2 chairs, while a monk asked me whether I wanted to give a blessing that would lead to a donation (which I don't really recommend as gifts are supposed to be spontaneous and not forced or encouraged).