The old observatory on Edinburgh’s Calton Hill may be the most favourably positioned art venue in the world. Recently resurrected by a group called Collective, the space, with its panoramic views and Enlightenment history, is an ambitious and imaginative addition to Edinburgh’s art scene.

In their Hillside gallery there’s a firing-range warning sign on the screen, a few seconds of stillness and silence, then a sudden machine-gun rattle. The sound is revealed to be a stick, dragged by a child along corrugated iron, and the juxtaposition is the strongest moment in Helen McCrorie’s portentously titled video work, ‘If play is neither inside nor outside, where is it?’ (until 6 October). The film shifts between lingering shots of children, poking sticks, hiding, climbing and wandering, and occasional glimpses of a data storage unit that is under construction beside the children’s outdoor playgroup, at a former MoD prisoner-of-war camp near Comrie in Perthshire. We’re meant to see a link between the ‘data gathering’ of undirected play and the faceless toil of humming computer servers. But it’s obscure and never quite moves beyond the observational.

The best video and sound stuff at this year’s festival is at the new Edinburgh Printmakers. ‘Deer Dancer’ is a perfectly pitched work by Hanna Tuulikki, shown (until 6 October) on two opposing screens and set to a bewitching and acutely atavistic sound track of thud and song and whoop. On screen, the artist, in a succession of fabulous costumes, plays multiple deer-inflected roles, dancing out a perfectly choreographed, rhythmic tale of hunt and kill. The antler headdresses, golden breastplates and furred codpieces add a layer of masculine idiocy to this Romano-Celtic pantomime. This is a confident, elegantly produced and richly layered work that translates something elemental about nature and ritual without ever edging towards the bombastic.

More disappointing is The Future is Inside Us, It’s not Somewhere Else, Nathan Coley’s show at Parliament Hall (until 25 August), and one of this year’s official commissions. Coley’s few pieces, awkwardly hung beside portraits of long-gone civic leaders, seem strangely lost amid the grandeur of the venue. In the capacious old hall, the artist’s illuminated phrases, cut into enlarged 19th-century wallpaper designs of an idealised North American landscape, are literally outshone by the stained-glass windows around them. ‘You don’t know about me,’ says one piece. It may as well speak for the exhibition, which has seemingly escaped the public’s notice.

So where are the art fans? Getting their eyes frazzled by Bridget Riley at the Royal Scottish Academy, that’s where. This huge retrospective (until 22 September) is a joy and, with its range of early works and exploratory studies, perhaps also a revelation for anyone who has, foolishly, dismissed Riley as a digital drone. Her work is fiercely analogue and, although deliberately free of painterliness in its construction, is the result of an intense relationship with the history and mechanics of painting. Riley wears her intellectual heft lightly, however, producing paintings of such adept precision and balance that the conceptual struggle behind them is all but invisible.

Each painting is built on opposition, light against dark, warm against cool, hue against contrasting hue. Forms assemble in a controlled progression of pace across the surface. Repetitions of pattern and colour are interrupted by subtle variations that introduce tension without ever collapsing into disorder, translating sensation into paint and then leaving the viewer to complete the picture.

Despite their almost Islamic sense of order, Riley’s paintings are demanding and interactive. The viewer’s eye will introduce additional colours, imagine movement and question solidity. The striped, coloured paintings appear to shimmer and shift, like the surface of water, while the monochrome ones dazzle and confuse with altered thicknesses of line implying improbable depths. The work is both static and active, uncertain yet described with absolute clarity.

Below the Riley exhibition, in the bowels of the RSA building, is The Paper to Prove it (until 8 September), a lively display of irresistible little David Mach collages and screen prints (see p. 27). A wild world, drenched in drama, is conjured out of cut-up comics, mostly old D.C. Thompson Commandos, with surreal encounters, tidal waves of exclamations and an explosive catastrophe around every corner.

A tribute to both the exuberance of comics and the quality of their original artwork, these assemblages, like Riley’s paintings and Tuulakki’s ‘Deer Dancers’, are the best of the festival, ingenious in conception and assured in execution.