When wintry sun slices down, sharp as an icicle, onto the extraordinary new staircase created by Rick Mather and his team for the Ashmolean Museum, the cliff of pale stone and glass is as beautiful as a piece of sculpture. Light floods into the new glass-fronted galleries, washes down into the basement, and trickles sideways deep into the labyrinth of the old galleries. In the dazzle, the newly cleaned portrait busts by Sir Francis Chantrey of long-dead worthies, stacked up three storeys high, seem to float free of their plinths and the wall behind them, an effect as startling as any piece of conceptual art.

This is the view chosen to illustrate many of the rapturous articles on the £61 million revamp which has truly transformed the museum. I loved every dusty hair on the old Ashmolean's head, but the beauty of what has been achieved is undeniable. The two new stairs and a web of glass bridges thread up and through all the levels of both old and new galleries. Although the architect claims to have overcome the deeply confusing layout of the old museum, on the busy Saturday we spent there visitors pored constantly over the floorplans, and consulted the notably kindly and helpful staff stationed at particularly baffling crossroads. Climb all six levels and you're rewarded by arriving at the seriously posh and beautiful new rooftop restaurant, where my teenage son read the menu with growing dismay, realising that even the chips are polenta.

Throughout the new building the glass walls, internal windows and recessed wall cabinets produce that cocktail party conversation effect of looking over the shoulder of the gallery you're engaged with and wondering if the next one doesn't look even more entertaining. Some of the picture galleries borrow more light from the stairwells than suits their subjects. The museum's extraordinary collection of Sickerts - including his haunting First World War view of glum Pierrots in Brighton performing to rows of empty deckchairs, because the lads who should occupy them are away being slaughtered in the trenches - is now in a room with one entirely glass wall. Mankind cannot bear too much reality, and Sickert, that darkest and most secretive of artists, doesn't benefit from too much light. The glowing Pre-Raphaelites might like it much better.

Some fabulous new treasure boxes have been created, of which the most beautiful is undoubtedly the textile gallery, displaying a collection that the museum never had the facilities to show before. The light levels are necessarily low, creating a sense of intimacy and excitement lacking in some of the other new galleries, which are as bright and shiny as Bond Street luxury shops. Gorgeous embroideries and tapestries, silks, velvets and ancient linens glow in the dim light. At its heart there is a large, elegantly lit case, with a bench opposite it (all the new galleries could do with a lot more perching space) so the visitor can ponder the extraordinary contents - a set of cloth-of-gold robes fit for a prince or a pope presented by Lawrence of Arabia.

The daylight draws you back out of the darkness to the stairs, and suddenly there is a problem with Chantrey's beautiful disembodied heads. The heads function superbly as a visual treat - but they barely function at all as museum objects. They are too high and bright to see the faces properly, or to admire details of the carving. Many came two centuries ago complete with bodies, which were later chopped off and stored or discarded as too bulky and boring to display. There may be a handsheet somewhere identifying them, but I couldn't find one. Along with new galleries still to open, much labelling or re-labelling is work in progress: some labels identify objects that haven't turned up yet, and many more objects still await theirs.

The heads sent me on a trail through the old and new galleries, to check how some of my very favourite objects have survived the Beaumont Street revolution. The best picture in the world, Uccello's Hunt in the Forest, is fine, as are the picture galleries generally: better lit, with new oak floors and wall coverings, so much smarter that they curiously resemble the Fitzwilliam's. On the ground floor another five-star collection has benefited dramatically from redisplay. It's hard to work out which of Ancient World/European Prehistory/Aegean World rooms might include Crete (come on guys - a bit of boasting wouldn't be out of place here: just say 'the world-famous collection of stuff from Knossos brought back by our former Keeper Sir Arthur Evans who pretty much invented the Minoans' and be done with it), but the new gallery is - mainly - a joy.

The old display was wilfully bad, with labels yellowed into near illegibility, peeling photographs, and the fabulous objects displayed apparently by the light of a 15-watt bulb. Now the romantic portrait of the young Evans is beautifully lit, the seal stones get a whole fascinating case of their own, and the massive ceramics are displayed at floor level and bravely uncased. Even here some odd choices have been made: argument may now rage as to whether the stone seat is indeed, as Evans believed, the oldest throne in Europe - but he certainly didn't find it with a 550-litre olive oil storage jar plonked inches away, as it now stands. The basement display on the history of the museum itself is so obviously work in progress I'll pull my punches: the mad cherishable treasures of the Tradescant collection, the seed from which the Ashmolean grew, are set out with all the flair of a jumble sale white elephant stall. A huge wall case is destined to hold the architectural models that are presently in a surreally dull and mercifully temporary exhibition upstairs. But if I come back in a year, and an object as fabulous as the hat Judge Bradshaw wore during the trial of Charles I - reinforced with iron because the regicide feared an assassin's dagger every time he left the house - is still shoved in the unlit bottom of a cupboard, I'll be seriously rude.

The England 400-1600 gallery I thought by far the worst. Like most of the new galleries, it's startlingly object-light. The cases are few, half empty, and overwhelmed by gigantic graphic panels: an ugly and not particularly useful timeline takes up most of an entire wall. There is probably every reason why glorious contemporary gold and garnet jewellery from a grave in Picardy has ended up a few feet from the Alfred Jewel, beside some rings from the 'Thames hoard' (what 'Thames hoard'?) and Henry VIII's tinder box, but the displays won't tell you. Alfred's wonderful confection of gold, rock crystal and enamel shares a handsome island case of its own with the little pointer probably made by the same workshop - but mounted at an angle so you can't see the back of it, and with the light casting a shadow blotting out the beautiful face of the saint, king or incarnation of the joys of sight. Halfway along the opposite wall is another of my best beloveds, one of the two Viking tombstones that used to stand, companionably chatting, in a sort of broom cupboard under the stairs. The label and the display do their best to drain every drop of blood from the marvellous object. The other, I eventually discovered, is now down in a basement gallery devoted to reading and writing: they both look awful in their new homes, and I feel they miss one another. The whole thing will bed down. The displays will be finished, all the galleries open. The basic bone structure is fine, and the graphic panels will go out of fashion and be junked - soon, please.

As darkness fell, l paused outside for one last look, and the unease stirred again. The great black double doors, tall enough for a giraffe to walk through without stooping, were flung back - the single most dramatic intervention Director Christopher Brown has made at the museum is opening the front entrance again after years when all visitors had to scuttle around the side like milkmen or bailiffs. The light shone out into the portico through the new double-height expanse of glass, with a revolving glass door at ground level. The effect was beautiful, the view through sombre entrance space into bright new atrium seductive. But from that angle I couldn't see a single museum object, and the battered old wooden reception desk has gone, replaced by a much smarter new one, out of sight to one side. It could have been the entrance to a smart café bar or a boutique hotel: it didn't shout museum at me, as the scruffy ink-stained beloved old Ashmolean did.