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There is a round house on the top of it, built in the 1790s, and a small temple beside it put up for the Royal Navy.

It is National Trust ground now and the walk up takes about half an hour. On a clear day you can see ten counties from it.

The round house on the Kymin was built by a dining club. A group of Monmouth gentlemen had been meeting on the hill every week through the summer, and in 1794 they started building so that the weather could not stop them.

They finished it in 1796 and added a naval temple in 1800, on the second anniversary of the Battle of the Nile. It carries the names of sixteen admirals, painted round it in panels.

Nelson himself came up in 1802 with Emma Hamilton and looked at it. He said it was the only monument of its kind to the Royal Navy anywhere in the kingdom, which was true then and very nearly still is.

Both buildings are still standing and the National Trust looks after them. The hill is about a mile east of the town and a steady half hour up on foot, or you can drive most of the way and park near the top.

The view is the reason to go. The whole of the lower valley opens out from the summit, with the river going away south into its gorge.

Come down the other side and you are looking across at the Forest of Dean, with the whole town laid out below you on the far bank.

The hill is National Trust ground and free to walk. The round house opens to visitors on set days through the season, so check before you climb if going inside matters to you.

The other half-day from the town is the Peregrine Path. It runs seven and a half miles from Hadnock Road out to Symonds Yat, along the bed of the old Wye Valley Railway, and it is flat the whole way. The town end of it is a few minutes from the middle of Monmouth, down by the river.

It is National Cycle Route 423, so bikes and pushchairs manage it as easily as boots. Forestry England shuts sections now and then after a rockfall off the cliffs above, so it is worth a look at the notices before you set out.

Canoes go in on the Wye at Monmouth itself. The usual runs are down from Ross-on-Wye or up from Huntsham, and the hire firms will collect you at the end rather than make you paddle back.

None of it needs experience. This stretch of the Wye is slow and shallow, with woods down to the bank most of the way. The only real decision of the day is where to stop for lunch.