Why do some memories stick out more than others?
First, whenever talking about memory, it helps to be specific. Memory is, somewhat controversially, categorized in a number of different ways. 

I'll take the liberty of assuming that you are specifically referring to episodic memory. Given your examples, we might even call it autobiographical episodic memory. 

Episodic memory is special in that it is a highly multimodal kind of memory. It's the kind of memory involved in "mental time travel", or the ability to retrieve a memory over many sensory domains and "relive" it. 

As such, there's a lot we don't know about why some of these memories are encoded more strongly than others. This is especially the case for events that we don't remember paying particular attention to, like walking to your babysitter's house. 

It could be, as you mentioned, that the emotional state associated with that event is strong.  Or, it could be that there's some combination of sensory inputs (sight, smell, taste, etc) that affect our bottom-up attention and are involved with being able to remember the event (Cabeza, 2008). It could also be that particular dynamic brain states are simply more "friendly" to encoding these memories (Watrous 2014), and your brain may have been in such a state at the time.

It's a very open question. If interested in this kind of memory, I would recommend reading Elements of Episodic Memory (Tulving 1983).

References: 

Cabeza, R. Role of posterior parietal regions in episodic memory retrieval: the dual attentional processes hypothesis. Neuropsychologia 46, 1813–1827 (2008).

Watrous, A.J., Ekstrom, A.D. The spectro-contextual encoding and retrieval theory of episodic memory. Front Hum Neurosci, 8 (2014)