You are spoilt for choice when it comes to things to do within walking distance of Willowford Farm.
Of course, there’s Hadrian’s Wall and all the Roman sites. [See also Hadrian’s Wall at Willowford and the Hadrian’s Wall National Trail.] Just one mile west of the farm is Birdoswald Roman Fort, called Banna in Roman times and then a fortified farm in the times of the Border Reivers, there is a visitor centre, cafe and extensive ruins to explore. Another 3 miles on from that is Banks’ Turret, the last remaining stretch of Wall before Carlisle.
Going the other way, 3 miles east is The Roman Army Museum and Walltown Quarry. Beyond that is Cawfields Quarry, then Steel Rigg and Crag Lough, Sycamore Gap and Housesteads. Just south of Housesteads is Vindolanda.
If you fancy a wooded walk on nearby stretches of the River Irthing there is Coomb Crags 2 miles west or just north of Gilsland is the Gilsland Spa woods with Sir Walter Scott’s famous Popping Stone and further upstream the impressive Crammel Linn waterfall. Or, on the River Allen there is Allen Banks and Staward Gorge.