"the price for an item is too high" - not a noun phrase. Actually, this is a clause, as it has a predicate of its own. "a bottle of water while strolling" - not a noun phrase. "A bottle of water" would be a noun phrase (a phrase that has a noun as a headword), but "while strolling" is an adverbial phrase that describes the verb "buy". "The same brand of bottled water" - noun phrase. The headword is "brand", and all the other words cling to it and provide additional explanation. "a pair of athletic shoes" - noun phrase. The headword is "pair".
