Unfortunately, to my knowledge, there aren't any direct ferries going along the coast from Valencia to Alicante. There are only the ones going to the Baleares Islands ( Mallorca / Ibiza ) from Denia or a nice one ( even though it's short) from Alicante and Torrevieja to Tabarca Island.
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There is a wide choice of transports that can either take you from one coastal area to another along the coast or inland. Making tourist stops is a fun way to the see the country, so scout around my accumulation of ideas and if you had been thinking about seeing the coast, you can take a cute train connecting Alicante with Benidorm up to Denia, enjoy its beaches and a good paella and then catch a regular train to Valencia from Alicante's central train station. It all depends on the time you have.
