One last one collecting my previous suggestions:

Neutrino Velocity Experiment

We detected a burst of neutrinos from SN1987a in the LMC. This is, so far, our only detection of supernova-based neutrinos. This event happened 180KPc away. If we can detect similar bursts from 10MPc away, we would be able to observe supernovae every few years, from varying distances away, enabling us to see how the peak get smeared out and/or delayed with distance. This would tell us information about the mass of the neutrino among other things.

I am not sure whether Ice-Cube will be detecting the right types of neutrinos to tell us this, but I hope so. Ice-Cube is not working with ultra pure water.

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Forming opinions as we speak