Where are the Fairy Fountains?

There are quite a few fountains overall, so they're fairly scattered. You're correct that some are close to dungeons, however not all dungeons have a fountain close by (e.g Water Temple) and not all fountains are near dungeons (e.g Hyrule Field).

Rather than copy out text, there's a list of locations for Great Fairy Fountains here and ordinary Fairy Fountains here. This is for Ocarina of Time 3DS, but I don't know if any of the locations have changed since the N64 verson.

Since you're just looking for healing fairies, you can simply get some by playing e.g. Zelda's Lullaby in front of a Gossip Stone (source). You can also play the Song of Storms to have a different fairy emerge which cannot be bottled but refills your magic, by the way.