I suggest trying the various Ys games. Ys I & II use classic top-down view but with a distinctive "bump combat" system that, in the modern "Chronicles +" release, is really perfected to make a very smooth and surprisingly fast-paced experience. Older versions of Ys I and II also work similarly, albeit with less polish.

Some of the other older Ys games may also fit the bill, but they've been replaced in the official Ys canon by their remakes, of which I'd suggest a trilogy of games that run on the same engine -- Ys VI: the Ark of Napishtim, Ys: the Oath in Felghana (the remake of Ys III), and Ys Origin (a prequel to the whole series). These are technically in 3D but they play in sorta pseudo-2D to some extent because you have a fixed angle isometric perspective most of the time.

By the way, all the Ys games are currently on sale in the GOG Summer Sale.

Also, you didn't mention Super Mario RPG, so I kinda need to mention it. :P Also, in a similar vein, if you don't mind the separation between action battle arenas and non-action overworld/dungeon navigation, try Tales of Phantasia, as well as the Summon Night: Swordcraft Story games.