You need to go to New Zealand. South Island.
Guidebook: http://www.paradise-press.co.nz/ppguides.html
Flight: expensive but worth it
Timing: February is good. I went Feb-April and had mostly good weather (other than wind, which you just can't get away from).
People: Friendly!
Services: towns are close together, food is good, water is clean, roads are reasonable. Many towns have "holiday parks" (=campgrounds) which may have indoor accommodations as well, like a cabin or bunkhouse. Holiday Parks have kitchens, almost universally, so you don't have to carry much cooking gear. Towns that don't have a holiday park may have a pub that rents rooms, and of course more traditional hotels.
Scenery: insane!
Hiking opportunities: world class, there are a bunch of "tramps" that get booked up months/years in advance, but I bet with some research you can find something. There are guide services and huts for some of these, that you are required to use, and I bet it would be easy to arrange transport of your bike (or you).
Other services - lots of hostels ("backpackers"), tourist bus services that can take you and your bike between towns if you want to take a quick hop by car.