For the first time in 23 years, the Turner Prize show has slipped its moorings and sailed up to Liverpool from London. By happy accident, this year's nominees - Zarina Bhimji, Nathan Coley, Mike Nelson and Mark Wallinger - all deal in themes that, right now, suit Liverpool to a tee.

Though their approaches are very different, each of the four explores the politics of spaces and places, and the way in which history, architecture and environment work together to affect and define us. Stand outside Tate Liverpool on the Albert Dock, looking toward the city, and the view resonates with the installations inside. The Liver Building is to the left, the Anglican Cathedral off in the distance, and in between a gaggle of cranes work to regenerate the river-front, slotting nondescript towers into the skyline.

It's a rich view, brimming with Victorian civic pride, haunted by ghosts of Empire and the slave trade, topped with unfettered progress for good or ill and serving to turn the Turner Prize show from a grubby competition into a group exhibition anchored in time and place.

Step into the gallery, though, and highfalutin ideas prompted by the setting begin to fade. You might think the show would rise to the occasion and make the most of Tate Liverpool, perhaps spreading across two floors, giving the four nominees plenty of room to breathe - there's nothing a northern city likes more than showing the southerners how it's done, after all. But no, the show is squeezed into a corner of the fourth floor, an airless, clammy and claustrophobic space.

This too, though, seems rather apt - the sense of impending disappointment raised by the cramped installation matches local expectations for the reason behind the Turner Prize show's move, Liverpool Capital of European Culture 2008, a project beset by administrative teething troubles that is limbering up to be a distinctly damp squib.

More than any of his peers, Mike Nelson stands up to the constraints of the space offered to him. This is a surprise. Nelson is best known for big, meandering installations that weave splintered narratives, blurring the lines between his work and the spaces it occupies. Here at the Tate, though, he's conjured up Amnesiac Shrine, a tight, concise installation that opens and closes with two near-identical campfire sculptures, crafted from charred sticks and flames of plastic.

In between is a maze of sorts. Four cubes stretch from floor to ceiling, each with an untidy peep-hole bashed into one corner. Inside, the cubes are hollow, piled up with dunes of sand, the interior walls mirrored to form an infinite desert landscape, overlooked, thanks to the mirrors, by the viewer's own blinking eye.

It is hard to resist flitting from one to the other in a bid to uncover previously unseen subtleties. This to-and-fro makes it easy to become disoriented, confidently striding out of the exit, only to find it's the entrance. The piece has a back-story, too. In the mid-nineties, Nelson invented a mythical gang of Gulf War veterans, the Amnesiacs, with whom he "collaborated" on a series of works.

While the resurrection of the Amnesiacs fleshes out the narrative of the Shrine, it doesn't feel central to the piece - visitors create their own story, and suffer amnesia of their own, lost inside the installation.

The same cannot be said of Mark Wallinger's Sleeper, a film, more than two hours long, which shows the artist, dressed as a bear, spending a few nights hanging about in Berlin's Neue Nationalgalerie. It's quite funny (men dressed as bears always are) but without the explanatory note that outlines Wallinger's concerns - which include the "sleeper" spies of the Cold War, an appropriation of Berlin's bear emblem by a foreign visitor and a satirical undermining of Mies van der Rohe's stripped-down Modernist building - we're left with a faintly amusing diversion.

And, once informed of Wallinger's aims, the work hardly improves, with interlocking concepts floating over it, not part of it. Like State Britain, his reconstruction of anti-war protester Brian Haw's banners and signs, for which he earned his prize nomination, Wallinger's Sleeper is a slight work, easily shrugged off, and no amount of curatorial justification can change that. Nathan Coley, on the other hand, makes dense, complex work that can speak for itself. His room is blocked at both ends by two threshold sculptures, oak beams that hinder the gallery-goer's progress. When last seen at Coley's solo show at doggerfisher, the threshold sculpture was slight and sly, a quiet suggestion to consider the space between spaces.

Here, he's beefed up the beams, so that they shout out an announcement that visitors are entering his gallery, an oddly aggressive gesture, undermined rather by the gallery attendant's constant requests that visitors mind their step.

There Will Be No Miracles Here, first seen on the Isle of Bute, is also transformed by this new context. The weak glow of the sculpture's gaudy fairground lights has taken on a deflated, sad air, offering a wry commentary on the Turner Prize competition, alongside the piece's existing associations. (The text is clipped from a seventeenth-cen-tury proclamation that ends "by order of the King", a curious clash between church and state).

Hope and Glory is another text made flesh, this time applying the patriotic English song to a model of a lowly terraced house, signs of its making still present on the surface, in stark contrast to the heavy metal plinth on which it sits. This is a distinctly ambiguous, ambivalent piece, and Coley, with typical economy, invites the viewer to tease out possible meaning - is it a denial of jingoistic bluster, or a tribute to honest patriotic feeling? Both, and a lot more besides.

Finally, Zarina Bhimji's photographs explore scenes of conflict in East Africa, hinting at horrors unseen. Illegal Sleep shows rifles leaning against a wall, and it takes a moment for their pleasing arrangement to fade, their true purpose becoming clear.

Similarly, it is the childish drawings scratched into the wall seen in Echo that draw the eye, only for a graffito that echoes Coley's work to heave into view: "The man which come from Congo should be killed by the order of the army."

So, who will win, and who should? For some reason, Wallinger is seen as a dead cert by bookies and critics alike, but compared with the other three, his work is weak, insubstantial and eminently forgettable. Just like last year's winner, Tomma Abts.

If the public had a vote and the prize were judged on this exhibition (they don't and it isn't), Mike Nelson would be a shoo-in: on my visit, the Amnesiac Shrine was met with squeals of delight and vigorous debate, with visitors lingering longest in his space.

Nelson, who, like Wallinger, has been nominated before, would be a deserving winner. And so would Coley and Bhimji. Though their reputations in the art world haven't reached the giddy heights of Nelson and Wallinger, both have forged rich practices, and it is their installations that linger in the memory, offering much to mull over after leaving the gallery.

Whoever takes the prize on December 3, the show is well worth the trip south. For once, it has the feel of a true group exhibition, with deep connections between the four selected artists, all in a city that suits them well.

  • The Turner Prize 2007 show is at Tate Liverpool until January 12.