In Which Layer, Dao or Service, Should I Parse a Rest Client Response?

Strictly speaking, Dao layer is used to manage information included in a persistence mechanism like: database, LDAP, etc So when you deal with an external endpoint, "include" that functionality in a service is an approach more widely used.

Answering your question, the first option is a better one.

  1. You are including the required business logic into the class that knows the returned format/information by the external endpoint.

  2. External classes that use the above one will manage a well know object (instead of a raw string value)

  3. Some types of upgrades in the external endpoint (changes in the response format, for example) can be better managed in your Dao class, without affecting to the other classes that use it.