Like the idea, particularly with the Sandy connection, but personally, that name reeks of "tl;dr" which for the older folks around here, means "Too long; Didn't read."
Your most memorable college sports rivalries generally follow Shakespeare and maintain that brevity is the soul of wit (Red River Shootout, Border War, Tobacco Road, Backyard Brawl, "The Game"). 2-3 words, alliteration. "Garden State Hardwood Classic" clocks in at 7 syllables, sounds like it was designed by committee and doesn't seem to fit that mold. If the branding is wordy, it better be creative: (See also World's Largest Cocktail Party or Clean Old Fashioned Hate.) However, no branding can save the fact that Rutgers and Seton Hall have combined for 1 NCAA Tournament win since 2001. That's ultimately what makes a good college rivalry.
PS: I'd have personally gone with "The Jersey War," but nobody asked me.