This post is so simple that it's almost cheating. In case you hadn't already thought of doing it, you can use the procedure outlined in my post on making paths through the wilderness to also generate rivers courses in hex maps. You can do this ahead of time or during play, as you prefer.
To make your rivers a little straighter, I suggest rotations of the d4 be to the second-next clockwise face that doesn't currently have a path on it (instead of just the next clockwise face, as per when you're creating paths).
I also suggest that any time you either generate something that looks absurd or that has 3+ streams flowing into a single hex, you make it a little pond or lake. Hexes adjacent to water-filled hexes count as having one stream flowing into them across the adjacent face if you're rolling for rivers. This will give you a handful of lakes and ponds of varying sizes.
I come from Canada, which has most (in the sense of a slight absolute majority) of the world's lakes, so I always think fantasy maps don't have enough open bodies of water of significant size on them, but this is a bit of an idiosyncrasy. If you do this procedure a few times across the length of the map, you'll eventually end up with a nice hydrological basin with rivers and lakes all connected up.