From the Barbican pontoon to the Royal William Yard:
Silverline water taxi operates daily from 10am – 6pm, until September, and offers passengers a unique water perspective of Plymouth. Departure times are hourly (on the half hour from the Barbican and full hour from Royal William Yard) with a cost of £2.50 for adults and £1.50 per child.
There are multiple bus routes all running from the city centre (Royal Parade) to The Royal William Yard/Stone House check Plymouth Bus 'PlymGo' site for details and journey planner:
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The Royal William Yard is a pleasant 30 minute sea view walk around The Hoe from the City Centre and, approximately, a 19 minute bike ride.