Unless you can get ingredients truly local, meaning the ingredients are actually produced locally, not just purchased locally, I don't think it matters too much. Fresh is good as euge said, especially for liquid malt extract. If you get liquid yeast shipped, make sure they can keep it cold (some places ship with ice packs for refrigeration), and try to get hops that are vacuum packed. I live in WA, so I can get all local ingredients (Hops, Malt, Yeast) and have in the past, its nice to have very fresh ingredients.
IMO, the best reason to buy from your LHBS is to support local businesses. I also like that I can make up a beer while I am in the store, and sometimes run it by another homebrewer for their taste imagination to "take a sip" of it.