Short answer: The Hoe is free, open and level, and gives the view that explains Plymouth — the Sound, the breakwater and the dockyard. Smeaton's Tower stands on it, a lighthouse moved here stone by stone. The Lion's Den below is popular when warm but heavily graffitied.
From the Hoe you see Plymouth Sound, the breakwater lying across its mouth, Drake's Island in the middle and the naval dockyard off to the west. It is one of the great city views in England and it costs nothing. Give it ten minutes before you start walking: the geography of the whole city makes sense from up here and it does not from anywhere else.
The red and white lighthouse on the Hoe is not an ornament. It stood on the Eddystone reef fourteen miles out, and when the rock beneath it started to fail, the tower was dismantled and rebuilt here stone by stone. You can go up it for a charge. The staircase is a spiral and it is not accessible.
Directly below the Hoe, the bathing area cut into the rocks. It is popular in warm weather and it is free. It is also heavily graffitied and the way down is awkward, so a good number of people look at it from above and leave it at that.
Clear evenings are the best of it, with the light going down the Sound and the breakwater catching the last of it. In winter it is exposed and the wind comes straight off the water, which is bracing rather than pleasant — but it is also when you get it to yourself.
The Barbican is a short walk east, the Box is up into the centre, and Royal William Yard and Devil's Point are west along the waterfront. The Hoe is the hinge the city turns on, which is why it is the right place to start a day here.
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