Here are two suggestions for nice day trips in the area around Tyinholmen. The peaks are easily accessible and they are also of such a character that you will experience a great view with nice nature experiences along the way:
Rusteggen is a characteristic reddish mountain ridge located up and northwest of Tyinholmen. There is easy access up the gorge from Tyinholmen - over Sukkenes bridge (large rock that lies over the stream from Sløtatjern) - further up to the crossroads between Skogadalsbøen and Fondsbu / Tyinholmen and then straight north and up the ridge that ends at the cairn at 1640 m where you has a majestic view of Skagastølstindene, Falketind and the Uranos Massif.
Estimated time: 5 hours
The nearest of the more characteristic peaks in the area around Tyinholmen - Breikvamsnosi rises straight up on the northwest side of Tyinvannet. Here you can choose to drive in and park by the third bridge - on the road into Koldedalen. The ladder then enters the left side of Koldedøla - and further towards the glacier fall on the first Koldedalsbreen glacier before cutting up to the left upwards along the ridge at Breikvamsnosi. Here it is a bit hilly and there may also be some snowfields that you have to pass. The trip then goes straight up to the cairn at 1720 meters and you have a great view over Tyinvannet and east towards Bygdin, Galdebergtind and Torfinnstindene.
Breikvamsnosi has in several places been described as one of Jotunheimen's most beautiful ski slopes and there is often snow here until well into the month of July!
Estimated time: 4 hours