You'll find a variety of music and videos on music topics (including performances of, e.g., full operas) in the database Alexander Street Press: Music & Performing Arts. that's available in our Databases A-Z. Just click on that link. When you access that from off-campus, you'll enter your Net ID and password when it asks for that.
As you may know, there are various commercial services and applications that are advertisement driven or fee based. Certainly explore to find one you like. You'll find a list of streaming music services in the Wikipedia article on Streaming Music Services, and a list of Internet Radio Stations in the Wikipedia article on that topic, and access to many streaming music options via iTunes, in both the "Radio" and "Radio" links.
Additionally, many public library systems in the Bay Area offer access to streaming music databases. Visit your local public library website for more information on how to access those resources. The following links are to public library collections that have particularly useful streaming music services.