Short answer: Plymouth has a mainline station and the whole waterfront works on foot once you are here. Ferries go from Royal William Yard to Cornwall and from the Barbican across the Sound. The thing you cannot do easily without a car is Dartmoor, which starts just up the road.
Plymouth is on the main line between Exeter and Cornwall, with direct services from London, Bristol and Birmingham. That puts it in a different category to almost everywhere else on this site — you can be here for a day trip rather than building a journey around it.
The station sits above the centre, so there is a walk down into town and a climb back. It is not far, but it is uphill at the end of a long day, which is the part people forget to budget for.
Royal William Yard has a ferry across to Cornwall, which turns a day in Plymouth into a day in two counties without a car. Services are seasonal and weather dependent, so check before relying on the return leg.
Boat trips leave from the Barbican and run round the Sound, out to the breakwater and past the naval dockyard. In a city built entirely around its water, seeing it from the water is the point rather than a novelty.
Royal William Yard is a walk or a short bus ride west of the centre and has restaurants, bars and a cinema in converted naval buildings. Devil's Point is just beyond it, with accessible paths and benches looking out over the Sound.
Dartmoor. The moor begins a short drive north and the bus services to it are sparse, seasonal and stop short of where the good walking starts. Dartmoor Zoo is the same problem — it is a drive. If the moor is the reason for the trip, Plymouth without a car is the wrong plan.
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