I've been looking through the files available at www.reactome.org along with some others but I only find images/pdfs of metabolic pathway diagrams. Where is the actual data these pathways are drawn from? I imagine there should be some kind of directed graph representation. I'm limited to freely available datasets, so unfortunately I'm not able to check out those such as KEGG.
KEGG is definitely your choice!
Then you can use these IDs to retrieve information about individual pathways: http://rest.kegg.jp/get/hsa00053 (GeneBank-like format), http://rest.kegg.jp/get/hsa00053/image (image), http://rest.kegg.jp/get/hsa00053/kgml (KEGG xml). It will take a while, of course, and I'd recommend not to overload their server and make delays between queries. With the GeneBank-like format batch querying is also possible: http://rest.kegg.jp/get/hsa00053+hsa00061
This should likely be a one-time or at least rare operation, because of the load on their server (and I don't think they make big changes very often). You can retrieve info for new pathways, once they appear in http://rest.kegg.jp/list/pathway/...