During his reign (August 117 AD - July 138) Hadrian did have a number of other accomplishments than his famous wall. He is well known for his grand building projects which included establishing cities throughout Egypt, Greece, the Balkan Peninsula and Asia Minor. In Rome he rebuilt the famous Pantheon (originally constructed by Agrippa) in 126 AD after it was destroyed by a fire in 80, built the Temple of Venus and Roma in 135 and funded the construction of many other buildings such as baths, libraries, theatres, villas and aqueducts. Although not the lead architect on any of his projects, Hadrian had a great interest in architecture and may well have contributed ideas and plans.
He finally completed the Temple of Zeus in Athens after 638 years of attempts by various emperors. He made other contributions around the city too and the Arch of Hadrian was built in 131/132 by citizens of Athens to honour him. He had a strong love for Greece and Greek literature and was often called 'Graeculus’ (Greekling) by his contemporaries due to this.
Hadrian was quite a well educated intellectual and although quite modest, was a talented poet and musician and as I mentioned before, a creative architect. During his reign he spent much of his time travelling the empire, around half of his time as emperor was spent on the road, something that was rarely seen. He saw his territories from as far as Britain to the deserts of Libya and was able to inspect issues for himself, he sought to gather first hand information.
Even though he supported slavery, he believed that slaves were treated with too much cruelty and harshness in the past and changed several laws regarding slavery. People who owned slaves no longer had the right to kill them, nor could they force their slaves into becoming gladiators or prostitutes. Slave labour camps were abolished. He also changed the law that stated that if a man was killed by a slave, all his slaves would be executed.
He was proven to be a capable military leader who had a good mind for strategy although he didn't care very much for war and favoured peace and security. Rather than expanding and conquering more land, Hadrian was more interested in consolidating and strengthening what he already had. One of his first decisions was to withdraw from a lot of the eastern territories back to the natural boundaries of the rivers Rhine, Danube and Euphrates and withdrew from Trajan's conquests in Mesopotamia and Armenia. He increased the strength of the empires borders by building fortifications in strategic locations - including Hadrian's Wall - and created a more disciplined army that he kept well supplied and well trained, in fact training and drilling was made more rigorous.
He felt it was important to not separate himself massively from his army, for example when he went on military campaigns, he ate the same food as them, even dined with them and slept amongst them. He could also be seen personally inspecting them at times.
Might have missed some bits out, hope I got most of it in there though!