Late August is a good time because the higher areas are covered in snow passed midsummer. So July is actually spring at high altitudes.
If you think about "hut to hut" hiking (trekking) for several days, then there are fewer choices, you should focus on one of the wider areas. Closest to Bergen is Stølsheimen area between Voss and Sognfjorden.
One of the widest areas is Hardangervidda, mostly easy trails (relatively flat area). Many access points by public transport, road 7 and Bergen railway cuts through part of the area, big glacier near Finse station.
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Jotunheimen is also very popular, more alpine, peaks, glaciers, sharp ridges and impressive lakes.
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SOuth of Hardangervidda (closer to Stavanger) you find "heiene", Setesdalsheien and Ryfylkeheiene. Most of this more modest altitude, wide, rolling hills. Ryfylkeheiene also includes the famous Lysefjorden:
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Use this for planning:
http://ut.no/kart