Being a Hilton, they are likely to have breakfast available. Not saying that it will be cheap, but I'd think that it's likely they'll have breakfast available. They may or may not have refrigerators in the room available.
There is a
Schnucks (local supermarket) that's not very far from EJD. However, they've branded it differently - I'm not sure if it's smaller with a more limited selection than a regular Schnucks or what. I'm haven't lived in STL in 6-7 years, so I'm not familiar with this particular store. Perhaps someone who is more local would be better to tell you what's different about this vs. a regular Schnucks.