I lived and cycled there for 6/7 years from 2000.
In terms of cycling the roads are in great condition and the only really busy road is the A road connecting Stromness to Kirkwall - even then only at rush hour times. I didn't find the locals to drive any worse than anywhere else. Most of the roads are quiet.
On Orkney going round the coast is a fair distance. Kirkwall is a good base as its central and has good facilities including a good bikeshop. It has a cinema, sports centre, lots of shops inc. Tesco. Stromness also has a bike shop. From Kirkwall you can do a circular tour west, north and south down to Burwick. there are good cafes in most places. Loads of eating places in Kirwall, Stromness and elsewhere. Great beaches, cliffs etc...
The main things to do are cultural (various festivals with the big one St. Magnus festival round about 20th June each year, also museums/galleries in Kirkwall and Stromness), archaeology, diving, fishing, sailing,walking, distilleries, breweries, viking related things, palaces (ruins), brochs, naval wartime info centre in Hoy, castles (Westray, Shapinsay)
From Kirkwall you can catch the ferries to most of the northern outer isles - probably Westray, Sanday are best for bike (Sanday for beaches). Rousay has a good circular route with a big hill. For Hoy you can sail from Stromness then cycle to Lyness for the naval wartime stuff and come back to Orphir.
The weather can be variable. It was the driest part of the UK last spring. It can be windy at any time, but it can be beautiful at any time. Big skies, few trees... Not any wetter than any other part of Scotland. Midges can be a pest in some places but usually there's a breeze. Natives are generally very friendly - there are a lot of "incomers" from the rest of the UK as well.
You'll get to like headwinds because you know sooner or later it will be behind you.