Some of the most rugged alpine heights in all Norway unfold along the spine of the heavily glaciated Lyngen Peninsula, east of Tromsø; you'll get the best views of them from the eastern shore of 150km-long Lyngenfjord. The peaks, the highest of which is Jiekkevarre (1837m), offer plenty of opportunities for climbers, but this challenging glacial terrain is strictly for the experienced.
The Lyngsdalen valley, above the industrial village of Furuflaten, is an altogether more accessible and popular hiking area. The usual route begins at the football pitch south of the bridge over the Lyngdalselva and climbs up the valley to the tip of the glacier Sydbreen, 500m above sea level.
Contact Den Norske Turistforening in Tromsø for hiking advice. The best map for hiking is Statens Kartverk's Lyngenhalvøya (1:50,000).