Let's take a look at the trajectory of variety probe missions.
New Horizons and Ultima Thule will be 4.1 billion miles away when it visits the Kuiper Belt object. This chart shows the path of New Horizons compared to other probes that have left the solar system. Credit: NASA/Johns Hopkins University Applied Physics Laboratory 
I wonder, why all these probes tend to explore outer system were launched to go outwards of the ecliptic plane instead of go upwards or downwards? What I'm talking about here is go upwards or downwards that is considerably closer to 90 degrees. I was told the ecliptic plane of any solar system tends to stay relatively uniform, with only Kuiper Belt Objects (KBOs) showing bizarre inclinations. The closest thing we'd find "below" the Earth would be an Oort Cloud object or outer star system, is it accurate to say so? What would we find if we go straight upwards and downwards?
Point of interest
1 Nola Taylor Redd, Space.com Contributor, January 2 2019, NASA's New Horizons Just Made the Most Distant Flyby in Space History. So, What's Next?