I think Buck has the right idea, I-80/I-95/I-295 to the Throgs Neck Bridge would probably be best, in spite of how nasty the Cross Bronx section is. However, the best alternate through Staten Island would be to take PA-33 south to I-78, then I-78 to I-287 to the Outerbridge Crossing, then NY-440 to I-278 to the Verrazano and Belt Parkway (NOTE - do NOT take the BQE!). You want to avoid I-280 when possible, it's a nasty road in its own right.