The River Hertford
In general, there are better options for north-south routes, with east-west perambulations more limited. That said, the banks of the River Hertford, owned by the Vale of Pickering IDB, can be passable especially between Star Carr and Folkton water treatment works. Though not a public right of way, it seems to be accepted locally as an informal path. It can get very overgrown, especially in summer but can make circular routes possible.
Several tracks and footpaths cross south to north. There is a public footpath, from Flixton to Seamer, which undoubtedly used to be a key route across the carrs before the modern road network. It leaves the A1079 west of Flixton village, passes Woodhouse Farm then crosses the River Hertford via a footbridge. Before doing so cast your eyes west, for this path passes right by the field under which the famous Star Carr archaeological site lies. You can easily miss it, for there is nothing presently to indicate the site, which is about 200m west of the path on private land. After the Hertford it soon joins ‘Metes Lane’, an old track up to Seamer (or you can link up to Crossgates).
Another good route leaves Flixton via ‘North Street’ which becomes Flixton Carr Lane, a wonderful green lane to its terminus at Flixton Bridge, right in the heart of The Carrs. Continue on a footpath north then choose either to head for Eastfield, or veer north-east to Grove Farm and Cayton via Carr House Lane.
There are also some nice networks of public footpaths around Staxton / Willerby Carr and between Muston and Gristhorpe/ Lebberston. Get your map or a good navigation app and and explore!
Short circular walks:
Start from Staxton village, take either Staxton Carr Lane (opp post office) or Ings Lane (past the school) northward and cross the Hertford footbridge to pick up the north-east footpath to Star Carr Farm bus stop on the A64. Here a Coastliner bus can take you back to Staxton to avoid the busy main road. (3km with bus, 6km without.)
Also from Staxton, or more accurately Willerby, explore Willerby Carr Lane to the river and railway crossings and the intriguingly named Robin’s Bottom Plantation. Retrace to the river and either take the southern bank or pick up the footpath connecting to Ings Lane or Staxton Carr Lane. (6 to 7km.)
There is a cracking 6km circular walk from Muston taking in part of the Wolds Way, (60m of ascent) with good views over the eastern end of the carrs. Follow the Wolds Way signs west out of the village, climbing up onto the Wolds. Then take a sharp right down the escarpment on the bridleway past Manor Farm, crossing the river, then east back to Muston. You could take in Gristhorpe for a longer route, adding another 4km.
Longer distance walks:
The Wolds Way (Yorkshire Wolds Way National Trail) offers views of the carrs from the top of the northern escarpment, before it descends to Muston and finishes at Filey, (where it meets up with the southern end of the Cleveland Way (Cleveland Way National Trail).
A lesser known walk devised by the late John Eckersley is The Coastliner Way, inspired by the bus route of the same name between Leeds and Scarborough / Whitby. This passes right across the carrs at Flixton and his website offers some additional insights you might like. Coastliner Way on the LDWA website
Wildlife watching – Ideas for the wider Carrs area for good vantage points for birdwatching or places to investigate.
Museums to visit – There are some great collections of artefacts from Star Carr in various museums near and far. Check first if they are still on public display or ask the curator.