Some of my preferred spots to fish by category:
River:
* Arrowhead Island. South off of the tip, where one of the Legendary Fish can be caught in the proper season.
* East/West off of the bridge leading to the beach, right at the zone line between the Town and the Beach. Useful mostly for grabbing that sunfish for the bundle on your way to a more profitable fishing spot Spring 2 when you just get the fishing rod
* East off of the small island south of Leah's cottage connected by the two bridges, on your way to collecting Spring Onions. It's faster to get here than Arrowhead Island, fish east off of the top of the island.
* Leah's shore, casting south into the river. Even faster than above, but due to how you tend to cast with more depth going east/west, the previous might be more 'efficient'. But it's a shorter walking path than the island, leading to more time available to fish, which probably offsets any marginal efficiency gained from the island.
Mountain Lake:
* Off the tip of the center island, where one of the Legendary Fish can be caught in the proper season.
* On the western shore of the lake, just before you start crossing the long bridge to get to aforementioned island, over by where Sebastian goes smoking, casting East into the lake, aiming at the log. It is a shorter walking distance than the previous spot, thus you can spend more time actually fishing instead of walking, and you're casting east into roughly the same general area, which may lead to some minor bonuses.
Ocean:
* Lonely Rock. You're casting West, so the east/west thing might give you more efficiency. It's a relatively short walk from the beach entrance.
* Off the pier south of Willy's. Either you can cast south from just outside his door, minimizing the time it takes to go to him to sell your catches before he closes, or fish east off the eastern side of the pier if you want to try to take advantage of the east/west thing. It's closer to Willy's if you plan on selling things as you catch them, but slightly longer to reach than Lonely Rock from the entrance.
* Off the Tidal Pool Pier. Some say you can catch different fish over there. I dunno. There is a Legendary Fish available here in the proper season, so there's that.
For the Hidden Forest Pond and Desert Oasis, it doesn't really matter, just aim for the middle of the body of water, even if it means casting at less than full strength.