Travel Itinary for New Zealand?

Travelling in motorhome in June starting and ending in Hamilton. Would like to see Bay of Islands, Waitomo, Taupo, Rotorua, Mt Maunganui.Only have 10 days so need a travel route that will cover these places in this time frame. Also whereabouts is snowboarding available in the North Island?

Snow boarding in the North Island is only available on the Central Volcanic Plateau. The 2 resort areas are Tukino and Iwikau accesible through Ohakune and National Park respectively.
Google them, and check prior to making the trip as there may not be any snow.
You aren't going to get far in 10 days.
Do not hire a motor home without a self containment certificate, or you may find you are not permitted to visit certain places.
You have no insurance if you take the mh up Ninety Mile Beach, so don't do it. Likewise the Russel Coast Road.
I suggest going up State Highway 1 to the Brynderwyns, then turn of to the Matakohe Kauri Museum.
On through Dargaville, through the Forest to Opononi on the Hokianga, then to Kerekeri, on to Paihia (from there take the coach trip up to Cape Reinga - leave your mh in Paihia for the day). Do a day's activites in the Bay of Islands, back through Kawakawa to Waiomio Glowworm Cave (don't put this off because everyone has told you to go to the Waitomo Caves, they are not a patch on the Waiomio ones), back through Auckland to Rotorua, via Waihi and Tauranga and the Mount. It'll take you 2 days to see Rotorua properly and from there you can go to Lake Taupo. The volcanic plateau and Iwikau village is but 2 hours travel from there.
Return to Auckland via SH 1 or up through Taumarunui and Otorohanga.
Check it out on maps, or go to www.googleearth.com
That's your 10 days gone.

I don't have a travel route to cover those places but snow boarding is available on Mt Ruapehu and the surrounding mountains, which are in the central area of the North Island.June would be a great time to see the mountains.

Doesn't the motor home rental place provide you with maps, travel routes, suggested itineraries?

The thing to remember is that NZ is a BIG little country.
You can't just zip from one place to another, there is lots in between. If you are planning on seeing those 5 cities and ending up in Hamilton you will be cranking. Please be careful on the road, take your time, and be a courteous driver.

Also be aware that "freedom camping" is no longer acceptable, except in certain, limited areas - and then there will be signs to indicate it is allowed. If there is no sign, then you cannot overnight there.

Have a safe trip and please do your part to help keep our country clean and green.

=)