You could say "sna cnoic" or "sna sléibhte", but if you use "hills" as the direct object (which is in the genitive case after a verbal noun) it sounds better.
The difference is quite subtle and not very easy to explain. "Ag siúl sna cnoic" makes it seem like the hills are just the incidental backdrop of your walking -- you're walking around, and you just happen to be in the hills. With "ag siúl na gcnoc", on the other hand, it's clear that the hills are the focus of your walking, that you're there specifically to walk in the hills.
"Siúlóireacht" and your example sentences are all correct.
You could also use the inflected verb (in which case the object is no longer in the genitive case): "shiúil/siúlann/siúlfaidh/shiúladh sé na cnoic".
I see you've been studying the past habitual tense:)