When you leave the town of Borgarnes in the direction of Bifröst (University Campus) pay attention after about 20-30 km. Two secret hot spots are well worth your visit in the neighborhood of Bifröst.
A little below Bifröst, on your left side, you'll find a road that leads to Hreðavatn, a beautiful little lake where it is possible to buy fishing permits if you wish. The surroundings of the lake are extremely beautiful and mostly hidden from Road 1. There are all kinds of trails available for short or long walks.
Glanni - Paradísarlaut
Another secret hot spot is also a little below Bifröst on your right hand side when driving from Borgarnes. Actually two spots to be precise! On your right side runs the river Norðurá with the beautiful waterfall Glanni. You'll find a nice walking path leading to it.
But don't just stop at Glanni... continue on the path until you reach Paradísarlaut - the Hollow of Paradise. A beautiful (and romantic!) oasis in the lava on the banks of Norðurá, not too far from Glanni.
Paradísarlaut is a hollow with a tiny lake in the middle with green grass, moss and bushes all around. You'll have to climb down a path to get down. A very romantic and wonderful place and if you brought some coffee and provisions, you can easily enjoy a small picnic there.