This is a "there-and-back" walk using, mostly, the Esk Valley Walk.
Navigation is vrey straightforward, although there is one point near the start of the walk where you need to pay attention to the map and to waymarks.
The ascents and descents are fairly gentle.
There are three stiles to cross on the field footpaths.

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A map of the route followed has been plotted on the Ordnance Survey mapping website, By selecting the ink below you will be taken to this map, - complete with distances and heights marked on the route.

OS Link

The route shown is on a standard map. To view the route on an Ordnance Survey map, select the icon in the lower right of the screen. If the route is displayed on a 1:50 OS map, zoom in to see the details on a 1:25 OS map.
There is also the option to view the route in a satellite image.

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Start from the station at Sleights (NZ867 081). There is limited parking in the street outside the station.
However, just nearby is a parking area which you may find to be more convenient.
From the station, head up Lowdale Lane and cross over the Iburndale Beck. Take the signposted footpath on your left along the edge of the cricket ground.
Continue ahead where the footpath leaves the cricket ground and continue up Echo Hill. Where the Echo Hill track turns right continue along the track until you come to a field gate. Pass through the gate and climb uphill at the edge of the field.
Turn left along the field footpath at the field boundary. The footpath is marked by a waymark on the right, set in the hedge. If you don't pay attention this waymark is easily overlooked!
Follow the clearly marked field footpath to Hagg House Farm.
At the farm, turn left and head downhill until you come to the railway track.
Cross over the railway line, turn right and follow the track to Ruswarp.
The track emerges outside Ruswarp where Oakley Bank meets Sneaton Lane on the B1416. Cross the road to take the pavement on the opposite side down into Ruswarp (CARE needed re. traffic).
Where Sneaton Lane meets Ruswarp's High Street, cross the River Esk on the road bridge.
Having crossed the River esk, there is now a permissive footpath that follows the Esk all the way to Whitby.
The footpath connects with the Marina car park.
From here head Northwards to the railway station, and to Whitby's pier and other attractions.
Return by taking the footpath from the Marina car park that runs beside the River Esk to Ruswarp.
From Ruswarp, retrace your steps to Sleights.
Alternatively, I Ruswarp you could take the road between Ruswarp and Sleights. However, this quite a busy road, with no footpath for most of the way. Not the ebst of options.