To find the most appropriate times to use a blockchain you should boil it down to what its core usefulness. An immutable, auditable, secure ledger that can be shared, blockchain has carved a niche for itself in the marketplace.
For example, typically it might not make sense to store data directly on a blockchain (this could vary and should be taken as a general statement) since a regular database could do it better; however, it might make sense to store Digital Rights on the blockchain and use the blockchain to securely transfer those rights, which are to off-chain data like music, since individuals could buy and sell data right securely with no middle man. It might also make sense to store computer code on the blockchain in which you could run a prediction market or a governance system that would be relatively fraud-proof.
Some general good uses/products of blockchain I would look at are music and DRM related projects. Filecoin and GNT are also interesting, and so is Aragon which deals with governance, gnosis, and Brave/BAT.