Wow, so many responses. Thanks to everyone for responding. So much useful information. So, I followed some of the advice and made the river flow into a larger river that flows on the outside of the mountains. Don't mind the ugly transition the river have, I'll fix up that later.

mapheight2.png

This does bring up a few other questions tough. How does this apply to ponds and smaller amounts of water like streams? As for the resolution, I'll bump it up to 5x when I render the final output. Currently have it low to save computing power. As for the size of the area. I'm not quite sure, but I'd guess that the full width of the area inside the mountains around 5-10 km.