The first time I was at Svalbard, we saw polar bears in the north (around Liefdefjorden), in the east (Hinlopen, Edge Island, Barents Island and Halfmoonisland) and in the south west (Hornsund and Bellsund). Some of them are at my flicker gallery:
https://www.flickr.com/photos/afoton/sets/72157629599971070I was mostly using focal length from 180 to 300mm.
The second trip was shorter, so we was just seeing one bear in the Liefdefjorden before we headed west for Greenland.
For looking polar bears, one have to travel far away from Longyearbyen. The easiest way is by boat, and that is also the safest way to come near a bear.