You have just described New Zealand.
In 3 months, you could ride on both islands, start on the south and work north with the season. There's nowhere on the south island I would give a negative comment about. (I rode very little on the north, and enjoyed it, but didn't cover very much.) East coast is drier and flatter (but not by any means flat). The west coast is very rainy, but still excellent, and there are so many hostels you don't have to camp in the rain. Scenery is spectacular and incredibly varied. Towns are 10-25 miles apart, most have a pub with rooms, a camp ground ("holiday park"), and/or a hostel. Don't bother taking a stove, camp grounds have kitchens, but you do need your own pot/plate/fork/etc. Roads are mostly chip-sealed (paved, but not very smooth) and totally fine for regular road touring tires. Traffic is light in most areas of the south island, most of the population is on the north island, but many roads there are also OK. There is some truck traffic but the truckers are good and safe drivers. The RV's in NZ are the size of a small van in the USA, so a lot less scary than here. It takes a couple of days to get used to riding on the left, but it's worth it. Very few dogs, and most are working dogs, well trained. No scary animals. No scary people. They speak english. The food and water are safe and fresh. You won't be the only cycle tourist.
Guide book: Pedaler's Paradise (one for each island)
Enjoy where ever you decide to go!