Personally, I would break it after Mr. Houston finishes speaking (your first example). This way, the first paragraph is about what Mr. Houston said, and the second paragraph is about the speaker's response, both in his thoughts and out loud.
He nodded. "Thank you for returning the bicycle. You see it was my son's and he would love to ride it one more time."
My heart pained at this, and I looked up at my dad, who seemed unmoved. I looked back at Mr. Houston. "Of course. I apologize I didn't give it back in time. I was scared."
This is just based on the dialogue you've posted. There might be a better way to do this depending on the rest of the conversation. For example, if you want to build a bit of tension, you might split it into three paragraphs:
He nodded. "Thank you for returning the bicycle. You see it was my son's and he would love to ride it one more time."
My heart pained at this, and I looked up at my dad, who seemed unmoved. I looked back at Mr. Houston.
"Of course. I apologize I didn't give it back in time. I was scared."
