Edinburgh Art Festival, Summerhall, Edinburgh

A former animal hospital turned exhibition space has an anatomical and visceral tendency, and there's plenty to see – if HMRC has let it all go yet

Kusmirowski's 'Pain Thing' at the former animal hospital Summerhall

Edinburgh being hilly and scattered and your time there possibly short, the opening of the Summerhall arts centre is good news. If you have a single day to do the city's Art Festival, then head for its ex-veterinary school, the Dick.

You'll know you're there because the bus-voice, worryingly, calls out "Dick Vet". This is the former animal hospital of Edinburgh University, now rebuilt out of town. Behind Dick Vet's mirthless Edwardian façade lies the most compelling new art space in Edinburgh, perhaps in the UK.

It isn't just that Summerhall is big, although that helps: during the festival, it will host some 30 shows of different sizes, entry to most being free. If Tate Modern's power-station past invokes the word "dynamic", then Summerhall's calls up a taste for dissection. So, too, does the unusual background of the gallery's visual arts curator, whose PhD is not in art theory but avian neurophysiology.

Combined with the ghoulish relics of Dick Vet's former life – anatomy tables, sluice sinks – this might have brought on a nasty case of Damien Hirst. Thankfully, it hasn't. Instead, the centrepiece of Summerhall's first full Art Festival is a rare British showing for Carolee Schneemann, in a show called Remains to be Seen.

A deeply intellectual seventy-something American, Schneemann has spent her career anatomising sexual archetypes. In 1963, her multimedia Eye Body shocked audiences by including images of its maker's own clitoris. This work will be reprised as a collage for Schneemann's Summerhall exhibition, along with a trio of video installations and new photographs of the artist ice-skating naked with her cat.

Alas, I cannot say what any of these works are like because they had been impounded by H M Customs when I went. "Intriguing" suggests itself as a word: Schneemann's Meat Joy (1964), watchable on YouTube, may give something of the flavour.

Border inspectors must have been napping when David Michalek's Figure Studies came by. A homage to Eadweard Muybridge, Figure Studies consists of three 3m-high screens on which are projected films of naked people, all volunteers. There are heroic young bodies of the Muybridge type, some very unheroic old bodies, male and female, and many kinds of bodies in between.

All these Michalek has shot with a high-resolution camera and then slowed the resulting movies down to glacial speed – his seven-minute segments are the outcome of five seconds of filming. The effect is curious: statuesque because of the porcelain finish of Michalek's monochrome film, but fragile because these are statues that move, even if slowly. Michalek teaches at Yale Divinity School and is married to a ballet dancer. Neither comes as a surprise.

In outbuildings behind the old Dick, the Belgian Neo-Pop artist, Jean Pierre Muller, has built what looks like a septet of Neoclassical beach huts. Each of these is a shrine to one of an eclectic mix of Muller's favourite musicians – Archie Shepp, Sean O'Hagan, etc. The effect is of a street of clinker-built recording booths, or an esoteric funfair. Behind these, Robert Kusmirowski, a Polish installation artist, has replaced Summerhall's natural ghoulishness with one of his own in a work called Pain Thing. Threatening machines and stable walls splattered with blood – actually coffee, as your nose will reveal – suggest a vivisection experiment. For all that, there is something unexpectedly funny about Pain Thing and its Grand Guignol drama.

What makes Summerhall particularly worth a visit is the breadth of what is on offer. Upstairs, a show from the gallery's permanent collection, Phenotype Genotype, contains vitrines full of art-historical bits and bobs, from a letter from Marcel Duchamp to a lover to scrap-paper artworks once sold by Tracey Emin and Sarah Lucas. On the classical side, there is a room dedicated to the Sixties conceptual group, Art & Language. On the entirely non-classical side are two contemporary shows on Summerhall's lower floors, one by boys and one by girls.

I cannot say anything about the second of these, OWWO (Only Women Women Only), not because it had been raided by HM Customs but because men are not allowed in. Well, I didn't want to see it anyway, so there. Women are allowed to see what Summerhall's curator refers to as "the Republic of Lad", although whether they will want to is another question. Static State wasn't finished when I went, but there were rumours of its participants, billed as nine of Edinburgh's most gifted emerging artists, having been seen photographing their own testicles. You have been warned.

Robert Kusmirowski to 26 Aug; all others to 27 Sep

Critic's Choice

With over 45 shows to go at, Edinburgh Art Festival includes blockbusters such as Van Gogh to Kandinsky: Symbolist Landscape in Europe 1880-1910 (till 14 Oct) and Picasso and Modern British Art at the Scottish National Galleries (till 4 Nov). Other must-sees include Dieter Roth’s swansong, Solo Szenen, at The Fruitmarket Gallery (till 14 Oct) and Mick Peter at the Collective Gallery (till 30 Sep).