I haven't cycled in North Park specifically, but I think the fastest way out of North Park and to the ocean is to take Texas Street -> Qualcomm Way -> Friars Road. Once on Friars, you have a bike lane and few intersections all the way to Mission Bay. From Mission Bay there's a number of routes in all directions.
Alternatively, you can take University or side streets to Fort Stockton and Presidio Park, it would be a more "urban" route with lots of shops, pedestrians and stop signs.