The Baltic Fleet is a brewpub. Bit grotty, but nice in its own way. I don't know if Liverpool Organic have a tap or do tours but their beer is always worth a punt if you see it.
Some fantastic ordinary pubs in Liverpool though, so no need to hit O'Neill's or 'Spoons. The Fly in the Loaf is craft beer heaven; just up the street there's The Phil with its legendary toilets and great pies. Dr Duncan's is Cains's tap and very nice. The Ship & Mitre also has a great selection, though it takes a while to do a full circuit of the bar to see everything that's on.