Base Camp - Walk from Base camp
I think it's called Tressenstein, will check in the morning with the map. But if you're at Base Camp it's the hill you see (on the right) if you look down the road (towards Bad Aussee) with the radio mast on top (ungrammatical). Anyway, it's a nice walk with amazing views. If you walk/cycle to the "Bad Aussee" town sign there are paths on the right, you want path no. 19. The sign says 2 hours, it took me 1 1/2 hours steady uphill (slowish compared to most) to the top. You can't really see base camp or Grundlsee, but you do get utterly fantastic panoramic views of Altaussee and Loser on one side and Bad Aussee on the other side.
The path is signed. I took a couple of wrong turns but made it in the end. Chickened out of climbing the mast but I bet you'd get a good view of Grundlsee from there. If you're festering at base camp and 2 1/2 - 3 hours to spare walk up this hill!! It's rude not to! Seriously good views, well worth the effort.