Stone fire places work very well both indoors and out. Stone is a good choice for building material around flames because it does not catch fire. However, firebrick is a necessary border between open flame and stone in order to prevent stone from cracking or exploding. I install firebrick in every wood burning fire place for this reason.
Stone has the additional benefit of holding heat generated by a fire. Thus, stone is able to radiate heat while the fire is burning as well as after a fire is out.
Most of the stone fire placeses I have constructed are designed for use with fire wood. A few others are designed for gas. Both types have benefits and drawbacks, and are worth considering to achieve the best fit for your circumstances.
For example, in a dry climate such as the southwestern US, an outdoor gas fireplace has a safety benefit of not emitting small embers of lit firewood. This can reduce the likelihood of an unwanted fire started from such embers. However, wood is a relatively sustainable source of fuel for a fire, and likely has less detrimental effects than the production and distribution of gas. Firewood also requires a place for storage, needs to be split and dried for burning efficiency, and generates ash that needs to be removed.