ころ, or ごろ (the colloquial pronunciation) is a word which carries the meaning of 'around', or 'about'. It is utilized in a similar way to くらい, but has a few differences. When ごろ is used, it will need to be attached to the end of a noun, or a noun followed by の.

• 11時（じ）頃（ごろ）に帰（かえ）ってくる。
  I will be home around 11.
• 私（わたし）は大学生（だいがくせい）の頃（ころ）に富士山（ふじさん）を登（のぼ）りました。
  I climbed Mount Fuji around when I was a college student.

The main difference between ころ and くらい is that ころ can be (and often is) used to express a broad point in time, while くらい is limited to expressing timeframes that are more specific.

• 子供（こども）のくらいはよく親（おや）と動物園（どうぶつえん）へ行（い）きました。
  When I was approximately a child, I often went to the zoo with my parents. (Unnatural Japanese, as being a child is a broad time frame)
• 子供（こども）のころはよく親（おや）と動物園（どうぶつえん）へ行（い）きました。
  Around when I was a child, I often went to the zoo with my parents. (Natural Japanese)

Conversely, ころ will not be used when expressing approximate distances/lengths.

• 2メートルくらいの所（ところ）に印（しるし）をつけてください。
  Please make a mark around the 2 meter point. (Natural Japanese, as an approximation is being discussed)
• 2メートルごろの所（ところ）に印（しるし）をつけてください。
  Please make a mark within the span of 2 meters. (Unnatural Japanese, as the listener would think that marking a line anywhere within the two meter space is fine)

The primary reason for this is that ころ expresses a span of something, while くらい expresses an extent. In this way, ころ could also be translated as 'within the span of (A)', while くらい is closer to 'at the point of (A)'. As an easier way to think about it, if we have a one meter ruler, ころ could express anywhere between 1 to 100 centimeters (the span), but くらい can only express somewhere between 90 and 100 centimeters (the extent).
Just like with English, if the 'time' expressed is very specific, then either くらい or ころ could be used naturally. This is due to the 'span', and the 'extent' already being something that is a 'precise point' in these cases.

• 今日（きょう）は12時（じ）くらいに帰（かえ）る。
  I will be home around 12.
• 今日（きょう）は12時（じ）頃（ごろ）に帰（かえ）る。
  I will be home around 12.