Switzerland is of course really expensive, but remember Australia ain't cheap either so I think it was less of a shock to me then it might be for someone from eg the US. I stayed with friends a bit which helped a lot.
Check out the Schwarzhorn which is a peak above Grindelwald with excellent views and some exposure. I went up the via ferrata and down the hiking route, which was a bit steep and loose (and with bonus snow patches for fun) but hopefully doable with a baby. The gondola ride from the valley floor is expensive so I caught a bus up to the Grosse Schedegg pass.
Also there's another peak called Tsuggen or something which looked good. There's also a hiking track around the green fields at the base of the Eiger which my friends liked.
Edit: it's Tschuggen and the Lauberhorn is on the same ridge. The Eiger base hike is called the Eiger Trail.