What are alternatives to Proof of Work for consensus of a blockchain that doesn't contain anything of value?
a blockchain that doesn't contain anything of value

Do you mean a blockchain with no associated token? If the data really has no value, no one will be interested in storing it on a blockchain.
If there is a limited amount of writers (i.e. up to ~100 nodes), it is possible to create a consortium network and deploy a blockchain using a Byzantine Fault-Tolerant (BFT) consensus (e.g. Proof of Authority). These blockchains do not require a token/cryptocurrency for the consensus. This is typically referenced to as a permissioned blockchain (as opposed to a permissionless/public blockchain such as Bitcoin or Ethereum).
Permissioned blockchains have different very different tradeoffs compared to permissionless blockchains. The blockchain is controlled entirely by permissioned nodes which are the only ones allowed to perform writes (in a public permissioned blockchain anyone is able to read). This model generally support a much higher throughput (more transactions per second) compared to permissionless consensus. Since nodes are authenticated in BFT protocols, the consensus model is designed to resists against malicious nodes up to a certain threshold (e.g. 1/3 of malicious nodes).
As a side-node, the flowchart in Fig. 1 from Do you need a Blockchain? can help to determine if a Blockchain is the appropriate solution for a problem.