"Everything is Brilliant in Leeds", at least it is according to the Kaiser Chiefs. The band's slogan is an unashamed promotion of their home city, an idea that has been eagerly snapped up by the city's new museum.

Leeds has been without a museum that tells the city's history for nine years, ever since the one that was crammed into the small space above the library shut up shop.

In the intervening period there have been changes of personnel at the top of the museum service, political control of the council has swapped hands, and there has been much to-ing and fro-ing between vested-interest groups keen to have their say about the shape of the new museum.

But in September the Leeds City Museum finally opened its doors. For most of its history, the building has played host to theatre of one kind or another. Many locals will have attended a performance or taken part in the children's theatre workshops there, so ascending the steps still has the feeling of a night out and the drama of the restored interior creates a thrill of expectation.

It is therefore a bit of an anti-climax to find the original auditorium is now a somewhat empty space. Half a dozen interactive podia are scattered over a large map of the city that covers most of the floor.

Overhead five large screens are suspended from the ceiling simultaneously playing a rather dreary video about Leeds, which amounts to little more than a tourist promotion.

This is the oddly-named Leeds Arena and it doesn't quite seem to know what to do with itself. There are no objects, it's not a performance space, it doesn't introduce the museum or the history of the city - so what does it do?

Well, it provides revenue-raising corporate entertainment space, although that's not much use to the average visitor, who rushes in hoping for drama, spectacle and wow but leaves disappointed after a few minutes.

There is very little to hold visitors here. The touchscreens play several films telling the story of dance in Leeds - the narratives are interesting, but they are all far too long. The shortest clip plays for four-and-a-half minutes and most visitors don't even last that long.

Once you get over this initial disappointment, things begin to improve. Also on this floor is the Collectors' Cabinet, which, as well as providing a home for the bits and bobs in the collection that don't fit anywhere else, allows the story of collecting in Leeds to be told. It's a nice combination of eccentric local collectors and the clubs that they formed, including the intriguingly named Leeds Savage Club.

The centrepiece is a dramatic recreation of Ralph Thoresby's Cabinet of Curiosities that takes up the entire end wall of the gallery and at last creates some of the spectacle that is so sorely missing in the Leeds Arena.

The nature of the building means that it was bound to be hard to navigate and visitors have to sweep back across the front of the Arena to the only other gallery on this floor, World View, which holds the ethnographic collections. The displays in this gallery will change but for the opening the focus is on Africa - a huge subject in a relatively small space.

There is a rich cross-section of objects on display and the interpretation is informative although unchallenging. To explain that some objects got into the collection simply because they were brought back by soldiers, sailors and traders somewhat underplays the role of British imperialism on the continent.

But there are some beautiful objects, such as a copper chest from Ghana, and interestingly there are some objects on open display that visitors are encouraged to touch, which goes some way to breaking down the traditional barriers between the visitor and the real thing.

While some ethnographic displays are content to keep their collections safely in the past, Leeds has made the link with contemporary Africa, which is welcome. But saying that Africa is not just about war and famine and then presenting a display which includes a Robert Mugabe flag, a red nose and a make-poverty-history wristband does undermine this message a little.

Downstairs in the basement is the Life on Earth gallery. It will undoubtedly be popular with families and is packed with interactives, stuffed specimens and bright colours. Here the museum is quite happy to answer questions about the how the objects got into the collection (Why do you have all this stuffed stuff?) as well as encouraging a more long-term interest (How do you become a geologist?).

The natural history collections are used to tell a number of different stories and displays range from a re-creation of a typical Leeds backyard, focusing on local wildlife, to a rainforest diorama. Evolution and Darwin are embedded in the displays, although the legitimacy of a section on creation stories, which asks visitors whether they "believe" in the theory of evolution, is questionable.

On the second floor is the Leeds Story gallery, which forms a semi-circle wrapped around the auditorium. The gallery is filled with a good mix of well-designed text and graphic panels, objects, a range of interactives, and layered information, including audiovisuals.

The story of how Leeds grew from a manor of about 200 people in 1086 to the massive urban sprawl that it is today is told fairly comprehensively via sheep shearing, dark satanic mills and back-to-backs. Visitors get a real measure of a gritty city that has reinvented itself several times over, and the stories of its citizens, some famous and some not-so, are dotted through the gallery.

The post-second world war story of the city is squashed into
a relatively small space and as a result is not told in much depth. This squeezing of modern history is disappointing, especially as sport, theatre and music - all major features of life in the city - are relegated to just a case each.

By this point you may want a cup of tea, and there's a fab cafe that spills out on to millennium square, but it's two floors down, so if you're going to do the whole show, you'd better keep going up.

The Ancient Worlds gallery occupies half of the third and final floor. The galleries are relatively small in scale, but this allows for an intimate experience with some wonderful and well-displayed objects (although whoever decided to put an excavation interactive with real gravel here will no doubt be cursed for eternity by the poor bugger who has to clean the carpet).

One of the stars of the museum is the Nesyamum mummy, respectfully displayed in a darkened chamber, which visitors are given a choice of entering.

From here there is only one space left and that's the temporary exhibition gallery that is reserved for charging exhibitions - currently one on Eating Creepy Crawlies. There is a logic in having the gallery here - visitors will have to pass the permanent galleries to get to it - and an obvious financial imperative for charging.

But when I was there I witnessed a stream of visitors approaching the entrance and then turning on their heels as soon as they saw the price (£9.50 for a family ticket).

I spent my formative years in Leeds and remember the old museum, so I couldn't be more delighted that the city has at last got its new museum open. But I want to be challenged more by the displays and would prefer a bit more of the gritty history and a little less of the civic pride. That said, the emphasis is clearly on family audiences and I am sure that it will succeed in attracting them in droves.
Project data

Cost: £20m
Main funders: Heritage Lottery Fund £19m, Leeds City Council, Yorkshire Forward
Exhibition design: Redman Design
Architect: Austin Smith Lord
Structural engineer: Buro Happold
Display cases: Click Netherfield