The place of residence shown for Mary McCarthy is Macroom. By the way, Maria is just a latinized form of her name used by the priest, not what she would actually have been called by her family. In fact, in 1836 she would probably have been called Máire, as the area was entirely Irish-speaking back then. Similarly, Patrick is listed with his name latinized as Patricius. Not all priests did that sort of latinization, but it was quite common.
Macroom is the name of a Catholic parish, a civil parish, and a town in Cork. When naming someone's residence, the priest would usually list the townland (which is a local area within a parish - not a town, per se), but Macroom does not appear to be a townland, or at least it's not listed as such at the townands.ie site. However, the townland names and boundaries back then had not yet been standardized, so some part of the civil parish may well have been referred to as the townland of Macroom back then.
Here's a link to where the civil parish is shown at townland.ie, with a list of the currently-recognized townlands:
https://www.townlands.ie/cork/macroom/
There does not appear to be any place officially called Emly in Cork today, although there are places called Emly in at least three other counties, the nearest one being about 40 miles to the northeast in County Tipperary. It's possible that the husband was from up there, and they met somewhere in between. Since the custom was to marry in the bride's parish, it would then make sense that the wedding took place in Macroom. However, this may once again be a case of a townland name which later disappeared, especially given the meaning of imleach, which is the Irish form of Emly. The word imleach refers to a marginal piece of land, so it could be that, back in 1836, there was a townland in Cork (presumably in or near the parish of Macroom) which was called that, due to its condition, and the name may have fallen by the wayside later on (maybe people didn't like the idea of their home area having such a disparaging name).