Harwich's drinking is concentrated in the old-town pubs — the Alma Inn on King's Head Street and the Hanover Inn on Church Street are the two most reliable, both serving local East Anglian ales and a regular flow of locals. The seafront has a couple of older pubs with terraces overlooking the harbour, useful for a beer on a long summer evening.
For coffee and cake, the small cafés around Ha'penny Pier and the visitor centre do the job; nothing in Harwich is far from anything else, so wander until you find a window seat you like.