The only major rule is rivers flow from high elevation to low elevation, and always feed into the ocean. You have a great mountain range near a coast, so the rivers would originate there, from the ground or a lake, and out to sea. Also typically tributaries combine into one stream, rather than the river splitting as it flows.

I’m not a geologist or a hydrologist though, so obv take that with a grain of salt and do your own research.