As a New Zealander I myself would go traveling during October as it is spring and a great time to travel. Many countries do not have a holiday at this time especially students and children as in many countries their school term would still be going.
I myself have travelled to Australia on several occasions during October of to Japan as it is very beautiful during autumn. I suggest anywhere in the northern hemisphere that is not too cold as it is Autumn there suggest countries would be Asia: Japan, South Korea and China. In the Americas mainly North America, USA Canada and Europe the Mediterranean such as Greece or Italy.
Yes, Austalians and New Zealanders stay in hotels however they may choose to stay in a motel, air BnB or backpackers if they choose to. The weather is rather mild at this point in spring so traveling within the country or overseas is a great option at this time of year.