If you're going for a North American-style city, I think the first thing you should do is consolidate the grid systems; the current map has half a dozen different grids which don't really line up where they meet. How does traffic get from the northwest to the southwest grid, when there aren't many intersections? If you consolidate the grids into one system, then other roads (parallel to the river, around hills, or so on) can be exceptions to the grid, but at most places the streets will line up.

I'd probably make the grid either straight north-south aligned, or parallel to the east-west road (which is a main national road?). The latter has the advantage that it's largely perpendicular to the river, so you can have avenues parallel to the river without too much interference with the grid.