I don't think this can claim to be a definitive survey; the exhibition is going for breadth rather than depth. There's a little information about his family background, and the relationship between the Uplii and the Aelii families (Trajan's and Hadrian's, respectively). Hadrian inherited an Empire at its greatest extent, but also with insurgency at its fringes; he withdrew and stabilised frontiers (including, of course, in Britannia). There is also a section on a Jewish rebellion around 130AD. Focusing more on his home life and achievements, space is given to the Pantheon, Hadrian's Villa at Tivoli, his lover Antinous, and finally his Mausoleum.
Highlights for me included the (modern) map illustrating the Roman, Han and Satavahana empires (and noting that there were trading links between them, if not political ones); some of the Vindolanda tablets (quite a few of the exhibits are credited to the Museum of Antiquities at Newcastle); artefacts from and a model of Hadrian's Villa; and some spectacular bronze peacocks believed to have stood on the perimeter of the mausoleum. Hosting an exhibition in the Reading Room (as was also done for the First Emperor) can be disorienting and claustrophobic, but also rather effective.