Brave new world beyond Rome's city gates Rome starts the new year celebrating modern architecture, with the exhibition on Le Corbusier's Italy continuing at Maxxi (00 39 06 322 5178; fondazionemaxxi.it) until 17 February on Via Guido Reni. It's an apt location - Maxxi is one of the city's few modern buildings, a stunning new museum of 21st-century art by Zaha Hadid. At first glance the façade still looks like an army barracks, but don't start this architectural tour at the original doorways. Walk left round into the huge piazza at the back of the barracks, to the starkly modern extension Hadid designed. It's here that it becomes obvious why Maxxi won the Stirling Prize for architecture in 2010. The gallery is made up of a sequence of corridors that coalesce, overlap and even leap over each other. Each is an enclosed routeway that merges at junctions or branches off. Maxxi redefines our idea of the art gallery as a sequence of rooms. Italy has a reputation for being at the forefront of domestic design - Alessi, Armani and Artemide - but the country's enthusiasm for modern architecture is less in evidence, simply because there is so much old architecture claiming our attention. In the 1960s, Le Corbusier planned a new building for Olivetti in Rho near Milan and a hospital in Venice but there was space for neither. When Maxxi was proposed it had to sit a kilometre outside the Flaminian Gate that has admitted visitors to Rome for more than 2,000 years. Inside the old city walls there's no room. Layers of great architecture pile up, almost smothering each other. Classical, medieval, Renaissance, Baroque, Victor Emmanuel imperial and then Mussolini, whose regime literally rebuilt the past in its own image. No wonder you have to come this far out to get a flavour of the new Italy. Continue east down Guido Reni towards Via Flaminia under maple trees; ironically the first building you reach is hardly modern at all. The Basilica of Santa Croce (00 39 06 322 2976; diocesiroma.org) may have been built in 1913 for Pope Pius X but it's self-consciously historicist in style, recalling an Italy of the early church. But as you get to the crossroads, modern and ancient Rome coincide perfectly. The new trams, with their passenger information shown on video screens, trundle down Via Flaminia on whose flagstones Caesar marched his troops into Rome 20 centuries ago. There's a little bistro here on an island between the north and southbound rails. Il Maratoneta (00 39 06 320 4840) is a tented structure where you can pause for coffee or a mozzarella sandwich for €5.50 (£4.50). On the other side of the tracks, Piazza Apollodoro opens up, a grassy area supporting a huge red modern sculpture of three interlocking squares by Mario Ceroli, a graduate of Rome's Accademia di Belle Arti. Ceroli called it Goal, presumably in reference to the Palazzetto dello Sport (00 39 06 3600 2439) which is the next building you arrive at across the tram tracks. The Palazzetto is a last vestige of the summer Olympics held on this site in 1960 (an event that launched a young American boxer called Cassius Clay on to the world stage). It's not a lovely building, but then the designer Pier Luigi Nervi was a pioneer of what can be done in reinforced concrete. This indoor venue was prefabricated in a series of concrete flying buttresses that were assembled here in 40 days. It's a low, space-age structure still in use as an athletics venue today and no doubt groundbreaking work, but I can't avoid the depressing impression that low ceilings have on human beings. As a species we respond positively to loftiness - think of Turbine Hall at the Tate Modern, or the Sistine Chapel, or any Gothic cathedral, and then think of hotel corridors from the 1960s where, on a good-hair day, your head is almost brushing the strip lighting. Fortunately beyond the Palazzetto dello Sport, after scooting under a modern flyover, you come to the other great icon of modern Rome. In 2002, Renzo Piano's Auditorium Parco della Musica (00 39 06 8024 1281; auditorium.com) was opened to the public, giving Rome the kind of contemporary classical music venue it needed. The auditorium consists of three halls with huge carapaces, aligned to the east, south and west. Piano linked them by a long glass-lined corridor. They look like a trio of armadillos involved in a stand-off. The space between them is known as Cavea and is used for outdoor concerts. Conductor, Antonio Pappano, is a regular visitor, having moved his Accademia Nazionale di Santa Cecilia here from a church near the Vatican. I must say this new bit of Rome impresses me. I wonder what Le Corbusier would have thought. Le Corbusier's Italy, curated by Marida Talamona, continues at Maxxi until 17 February Rome's gallery of modern art GNAM (00 39 06 322981; www.gnam.beniculturali.it) reopened at the end of 2011. Though its exterior dates from 1883, the approach to exhibiting art inside is very new. From 1 February the museum will be hosting a new exhibition about Vittorio de Sica, the neo-realist director who made Rome cinematically famous in Bicycle Thieves. JK Place Rome is a new hotel opening in the heart of the city this spring, just off the Via Condotti. Expect sleek, modern design in a historic building (jkroma.com). You can reach Rome by train in a single day from London, with changes in Paris and Turin. Railbookers (020-3327 2439; railbookers.com) offers three-night city breaks, out by train, back with British Airways, with bed and breakfast accommodation for £649. Rome has two airports: Fiumicino, served by Monarch (0871 940 5040; monarch.co.uk), BA (0844 493 0787; ba.com), Alitalia (0871 424 1424; alitalia.com), easyJet (0843 104 5000; easyjet.com) and Jet2 (0871 226 1737; jet2.com). Ciampino, slightly closer, is served by Ryanair (0871 246 0000; ryanair.com). Hotel de Russie, Via del Babuino 9, Rome (00 39 06 328 881; roccofortehotels.com). Doubles start at €369 (£300), including breakfast. Italian Tourist Board: 020-7408 1254; italiantouristboard.co.uk