As I left Coventry's newly refurbished and extended Herbert Art Gallery and Museum on a gloomy winter afternoon, I was trying to remember if I was already feeling mildly grumpy when I'd gone in a few hours earlier. The visit started well enough.

Extremely helpful front-of-house staff, a decent - if surprisingly pricey - lunch in the museum cafe and a general predisposition to be positive about new experiences.

So what, if anything, had gone wrong? Was it, perhaps, my inability to recognise and appreciate what may have been intended as absolutely cutting-edge ironic post-post-modernist display? Have I become so accustomed to Heritage Lottery Fund makeovers that the fix needs to be better and stronger each time before I can get a hit?

The problem, I now realise, is one of general, and occasionally disastrous, over-design. There is nothing wrong with the architecture of the Herbert. Opened in 1960, the original building is a more-than-respectable example of postwar municipal modernism, with clearly articulated galleries and, following a first phase of redevelopment that opened in 2005, some decent public spaces.

Underlying the latest extension and refurbishment was the need to meet the requirements not only of the museum and gallery, but also of the city's media centre and archives, which are now housed there.

The 2008 build, designed by Pringle Richards Sharratt, felt to me rather derivative (Hopkins via Grimshaw and Calatrava with just a pinch of Gateshead's Sage concert venue), but it does a competent job of providing a flexible new double-height entrance foyer, a History Centre, local history and temporary exhibition galleries and access to the amazing medieval undercroft.

So no real problems with the building itself, then. Neither, as far as it was possible to tell on a Saturday afternoon when the History Centre and most of the education and media spaces were closed, with the commendably broad public provision.

Brief chats with other visitors and staff suggest that the citizens of Coventry are well pleased with the enhanced provision. No, the problems, for me at any rate, are largely to do with the design and therefore the overall experience of the galleries themselves.

Take the new History Gallery. Entrances at both ends make a nonsense of the overhead timeline - which would have mattered more if anyone had been trying to follow it. The display is organised under narrative headings, but there's no indication from the designer as to one's immediate whereabouts in the overall story.

In the end, it's much better to do as everyone else seems to be doing and follow your eye through the chaos to something which grabs your attention, in the assumption that you'll eventually emerge with at least some idea of the long history of this fascinating city.

With the now obligatory children's trail, personal reminiscence and oral history points, the undeniably rich collections are presented in a manner redolent of Newcastle: Great City. But what felt excitingly innovative on Tyneside in the 1980s seems sadly passé in the Midlands 20 years on, and there's surprisingly little reference to
the evolution of Coventry's rich cultural and ethnic makeup.

Above the History Gallery are usefully neutral temporary exhibition and studio spaces, linking the new building to the original at first-floor level. There's a nicely positioned piece by Mona Hatoum outside the excellent unisex lavatories, opposite a Barbara Hepworth sculpture with a label encouraging youthful engagement with the art ("Can you think of other things with holes in them?").

One of the best installations is the Old Masters Gallery. Relatively few of the works may be recognisable old masters, but the hang is excellent, as are the clearly explanatory, but not overextended, labels and text panels. The galleries displaying representative sculpture, and art since 1900, are fairly traditional and seem to work well for visitors.

Then there's the Elements (natural sciences) Gallery, in which the exhibition designer has pulled off something exciting.

The interactives are very effective and, in one or two places, the display enhances the collections, rather than overwhelming them as it does almost everywhere else.

The original main staircase glides elegantly down to a lobby where there's a metalwork installation, with a nice selection and juxtaposition of objects from stuffed birds to modern ceramics. But why hang a charming sampler so slightly off the vertical that it looks as though someone has mislaid the spirit level?

The integral seating arc looks (and is) pretty uncomfortable and offers ample opportunity for bruising shins and ankles, so go quickly into the Peace and Reconciliation Gallery, where an excellent curatorial hand has resulted in something genuinely moving and thought-provoking, despite the sub-Libeskind design shards.

Next door, Discovering Godiva is great fun and offers an opportunity for a discussion of the relationship between history and legend and a nicely-judged storytelling corner.

If there's a real star here, it's the outstandingly high quality of the Herbert's new text and printed materials. The gallery text is hard to fault and both the 50-page souvenir handbook and the 12-page gallery guide are near-perfect. Carefully pitched, informative and well written, the Herbert's text deserves to become a model of excellence.

It's just such a shame that exemplary curatorship, great writing, accessible thinking and good intentions have so often been swamped by excessive design. But if you want to clear your visual palate afterwards, there's always the cathedral across the square.

Nichola Johnson is the director of the Sainsbury Centre for Visual Arts
Project data

Cost: £20m
Main funders: Coventry City Council £9,293,000, Heritage Lottery Fund £4,874,000, European Regional Development Fund £3,532,000, Department for Culture Media and Sport/Wolfson Foundation £342,000, Renaissance West Midlands £178,000, Advantage West Midlands £196,000, English Heritage £20,000
Architect: Pringle Richards Sharratt
Exhibition design: Event Communications
Lighting consultant: Martin Klingler Lichttechnik
Project management: Gardiner & Theobald Management Services
Cost consultant: Turner & Townsend
Main contractor: Galliford Try Construction
Exhibition fit-out: Edwin Dyson and Sons
Exhibition lighting design: Full On
Exhibition mounts: Plowden and Smith
AV Software contractor: Elbow Productions