I've thought a lot about this, and it's likely the reason I have terrible mosquito problems...

This "river" collects to this...

MOST of the water goes into the tough that was build to prevent the water from hitting the foundation too much. But like you can see, a lot of it gets trapped behind the retaining wall.

This is another angle of it coming down the tough. This empties into my side yard.

I've thought about putting a large curb along the back of my yard, all draining into one spot (at the top of the yard where most of the water enters), then running 3-4 none perforated drain pipes down my yard, around the side of my house, and down to the street.

But I'm open for creative ideas....

Thanks in advance!

And yes, this is a BIG job not at all DIYable unless you have access to backhoes and dumptrucks AND are a landscape architect.

Regrading and adding subterranean drainage are both options. Landscapers and the city engineers are good sources of information. This might fall into a plumbers' area of expertise.

Here is a scanned image of the backyard with new ideas on how to curtail the yard.

Each red circle is an drop inlet for water (also where the river entering my yard starts) and the little black circle are river rocks to prevent erosion and filter other peoples' yard debris from slowing down water flow. Red arrows are slopes. The green line is likely going to be an 8" smooth storm water pipe (corrugated, would likely be too turbulent for the amount of flow I have). The green line going down would connect into the county storm water drain in the front of my house.