As I understand it, Thomas Halliday who built and owned the now defunct Robin Hood spent a great deal of time in his favourite place which was Matlock in Derbyshire. He wanted to recreate the look and feel of Matlock and planted many of the trees and laid paths in what we now refer to as Loxley Woods. This area then became popular with his friends for strolling around on Sundays especially in summer.
ps, just found this interesting article
By Henrik Thiil Nielsen, 2013-08-07. Revised by Henrik Thiil Nielsen, 2018-07-12.
Around 1800, the Reverend Thomas Halliday, a local Unitarian minister and something of an entrepreneur, was so struck by the beauty, and similarity to Matlock in Derbyshire, of a spot along River Loxley then known as Cliff Rocher that he set out to transform it into Little Matlock, a name it retains to this day. Not content with altering the name, Halliday, spending his wife's inheritance, had stairs and paths cut into the rock and let trees and shrubs plant in order to accentuate the similarity to the picturesque valley in Derbyshire. The area was then opened to the public and for a few years attracted large numbers of visitors from Sheffield every summer.
In 1799 or 1804, Halliday built a house, one half of which was from the start used as a public house, the Rock Inn. However, the exact year is not the only point of disagreement, for according to the pub's website and a local newspaper article, the pub retained its original name till after the Great Sheffield Flood of 1864 and was only renamed the Robin Hood at some later point. On the other hand, a user-edited Sheffield history site, listing evidence from some thirty trade directories spanning the period 1833 to 1951, knows the establishment only under the names "Robin Hood" and "Robin Hood & Little John". Contributors to that site think the pub opened in 1833. To this we may add that there was already a "house of refreshment" in 1824 (cf. 1824 Evidence below) and that an 1845 trade directory lists the establishment as "Robin Hood and Little John, [proprietor] John Rusby, Little Matlock". This latter source does not mention Rock Inn. Finally, we note that Harrison refers to the establishment as Rock Inn in 1864 (see Evidence below), long after it first appeared in the records as Robin Hood (or similar). Unless the Robin Hood and Rock Inn were in fact two different establishments, we must conclude that locals continued to refer to the Robin Hood as Rock Inn more than thirty years after it got its new name or that perhaps Harrison used the old name out of habit. In any case, the Robin Hood Inn closed on August 28, 2011.