The stone is located in the volcanic tundra between Windhelm and Riften, just outside the mountain range between the two locations. Near the Eldergleam Sanctuary and Darkwater Crossing, the stone is by the river to the South-East.
The magicka regeneration decrease may appear to be a disadvantage at first, but when combined with the Recovery perks, the drawbacks can be negated, with the added benefit of an extra 50 magicka points and 50% spell absorption.
When combined with the Magic Resistance and the Atronach perks from Alteration and the Elemental Protection perk from Block, it is possible to build a character that is highly resilient to magic.
As a Breton, the Dragonskin power will stack with the Atronach Stone, making the player immune to magic for the duration of Dragonskin.
Also given the way the magic regeneration system works, with the more magicka a character has, the more they gain per second. So with a 50% reduction to magic regeneration, the two ways to counteract this effect is to either get another 50% regeneration effect OR double the magicka capacity.
For another, slightly unorthodox, strategy, this stone can be used by a pure combat character who does not use spells. The slight stunt in magicka is rendered irrelevant, while gaining powerful Spell Absorption. The magicka boost, however, is wasted in this situation.
Always add 360 , PS3 , or PC to clarify which system the bug appears on.
Click to see the list of bugs encountered
PC 360 PS3 Unfortunately for Conjuration mages, the game treats summoning as a spell being cast on yourself, thus the 50% spell absorption chance kicks in making your summons 50% likely to not occur. PC Users can avoid this bug by installing the "All in 1 Spell Fixes Mod" 
PC 360 PS3 As a bonus, when a summoning spell gets negated the player will "absorb" the magicka, this can be used to restore a low magicka level. However, since 50% of the time the spell still works normally, it can take a few tries and you also must have enough magicka to actually perform the spell.
360 Interestingly enough, when using the Dragon ShoutSummon Durnehviir, should it fail the player will regenerate all their magicka, due to the game treating the Shout as a Conjuration Spell.
In some instances, the 50% spell absorption also intereferes with the Elemental Wall spells (Flames, Frost, and Storms). When casting the Wall spell, the wall appears sporadically, and often not at all.
You can combine the magicka absorption with the shielding circle spell for infinite magicka while inside the circle.
PC 360 PS3 The 'absorb' animation used for showing that an enemy's spell is being absorbed can also play incorrectly for non-magical attacks. This has been observed with everything from non-enchanted swords to a wolf's bite. The reason this occurs is because wolf/bear attacks have a chance to inflict a disease such as Rockjoint, so their attacks have a magical component (each time the animal attacks it casts a spell on you with a small chance to inflict a disease). Thus, the Atronach Stone reduces the chance for you to receive a disease from these animals by 50%. (All platforms)
The spell absorption effect may cause problems during Brelyna's Practice. In the quest a spell is cast on the Dragonborn, however if the spell is absorbed then the quest will not progress any further.
A potential solution for the spell absorption interference is to place the Atronach Stone on the Aetherial Crown, so that the Stone's effects can be equipped and unequipped as needed.