Recently, the Pocket Bard app for music and ambiance. You can select a setting like a town, dungeon, forest, etc. and it will pick thematically appropriate music. It has an intensity slider that will subtly change the music on the fly, becoming more soothing/playful at low levels and chaotic/dramatic at high levels. You can switch between exploration and battle music depending on what players are doing, there's even victory music for after a battle.

It's definitely a step up from shuffling between various YouTube playlists.