You can install a french drain system, like on a septic tank. Basicly its a trench anywhere from 25 - 50 feet long with a perforated pipe in it. Then the pipe is coated with a sand sock and the trench refilled to within 4" of the top with gravel. A layer of filter paper is laid on top of the trench and the final 4 inches is refilled with black dirt. Grass can be grown on top of the trench. Your sump pipe is inserted into the end of the drain field. Of course if your soil is heavy clay, it will not work. But if your soil is any mixture of gravel, clay, and sand, it will work fine.
This will probably cost you as much as running it out to the sidewalk though.