The Barbican is worth checking out, expecially if the weather is good. From there you can visit Cap'n Jaspers to buy a Jasperizer or catch the water taxi across to Mount Batten. There is also loads of touristy places like the The Nation Marine Aquarium and the Plymouth Dome.
Though quite why you'd want to do that when you could just get pissed up until 6am in the diviest dive in Divingdom I don't know.
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