The best rpg games like Skies of Arcadia are Grandia II, Sea of Stars and Chrono Cross. Below are 9, each with the reason it is here — and, at the end, what filtering to rpg costs you.
Filtering to RPG means you want progression — a character to build or a party to grow — layered on top of whatever else you liked.
What you get: A reason to keep going after the novelty wears off. RPGs are the genre that reliably converts hours into feeling more capable.
What made Skies of Arcadia worth playing in the first place is covered on the full list. This page is the rpg part of that answer, and only the rpg part.
Same era, same warm tone, and the best action-timeline battle system of the generation.
A modern turn-based RPG with the same bright, adventurous mood.
Sailing, discovery and a soundtrack people never stop mentioning.
Sega's other great RPG, and it holds up remarkably well.
GameCube RPG with floating islands and a card-based battle system.
The entry in that series that shares Skies of Arcadia's optimism.
Same generation, timed-input combat, similar earnestness.
A remake that keeps the exploration and the warmth.
For the sense of a world that keeps opening outward.
Immediacy. Almost every RPG asks for a slow first few hours, and the systems that make hour forty good are the same ones that make hour one a menu.
The full list is on games like Skies of Arcadia — 9 picks, no genre filter.
Grandia II. Same era, same warm tone, and the best action-timeline battle system of the generation.
No. Skies of Arcadia released on the Sega Dreamcast, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Whether the stats are the point. In an RPG the build decides what you can do; in an action game with stats the build only decides how fast you do it.
No. The picks below span turn-based, real-time and action RPGs, and each one says which it is.
By hand. Each pick was written for the full Skies of Arcadia list first, on what the game actually does, and this page is the part of that list that is rpg — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the rpg guide for where to start in the genre generally.