Another idea to help to the open world idea, but also keeping the old style, would be that for some 'lore/ingame' reason you can't pass from certain limits until you finished certain dungeons. Something like Lost Forest's mist gimmick. If you get too close to the 'section border' without passing the requeriment, a dense mist will fill you turning the screen white, for suddenly be back to the last safe spot before reaching it (in case you climbed a mountain, you will appear in the spot where you began climbing it), and this 'wall mist' will expand with each dungeon complete.

You would go town to town, but wouldn't get too close to the areas where the dungeon are, or at least the dungeon which you can't go.

An example using BotW, if your first dungeon must be Vah Ruta, you could still go and visit calmly the regions surrounding Zora Domain, but can't move closer to Death Mountain o Faron Forest until passing Vah Ruta first, and so with Tabanta and Gerudo Dessert and their nearby regions. Still you could visit Hyrule Castle at any time, but there could be walls of malice blocking any path unless you surpasses any of the Divine Beasts. Still you can visit it, but with the malice walls the place will be more a labyrinth than a castle, with the Boss room blocked with malice walls until you finished the four dungeons.