[noun (time)] + ごろ [noun] + の + ころ [verb (plain)] + ころ [i-adj] + ころ [na-adj] + な + ころ
頃 marks a time. Straight after a clock time or a date it is read ごろ and means "around"; after の, an adjective or a verb it is read ころ and means "the time when", "back when".
ころ names a stretch of time rather than a moment – a time of your life, a period back then. A noun takes の before it, a な-adjective takes な, and a verb is in the plain form: the た-form looks back, the dictionary form is "around when it is about to happen".
"At that time" is そのころ, and "back then", looking back with some feeling, is あのころ.
ごろ goes straight after a clock time, a day, a month or a year, with no の. に after it is optional.
いまごろ今ごろ means "about now" or "by now", often in a guess about what someone else is doing.ごろ marks only a point in time. For a length of time, the word is ぐらい.
In conversation ぐらい also goes on a clock time – さんじ3時ぐらいにあおう会おう – so the mix-up only goes one way.