Big ticket neighbour: Miami, Florida

If Florida has an equivalent of the Gold Coast, Fort Lauderdale is it. Popular with both families and rowdy students at the end of the school year, Lauderdale also has miles of sandy beaches and a massive network of waterways. The latter are lined with lavishly expensive houses, and cruises go past, spilling all the salacious gossip about the multi-millionaire home owners. It's a place that can make you very jealous very quickly if you don't just throw yourself into the bling-flinging. See sunny.org.

See: What to do in Fort Lauderdale

Padua

Big ticket neighbour: Venice, Italy

In equal turns gritty and pretty, Padua has three extraordinary sights worth making the trip for. The first is the world's oldest botanic garden and the second is the Palazzo del Bo – the main university building which houses the world's first anatomical theatre. The latter is entirely made of wood, and is staggeringly atmospheric. Then trumping the lot is theCapella degli Scrovegni, which is covered almost entirely by Giotto frescos – making it a single giant masterpiece. See discoverpadova.com.

See: The three-minute guide to Padua

Vicenza

Big ticket neighbour: Venice, Italy

Architectural uniformity makes Vicenza compellingly striking, and it's largely down to one man – Andrea Palladio. His takes on ancient Roman architectural forms created countryside villas and in-town palaces that were marvellously harmonious with their surroundings. His two greatest set pieces – the double loggia-boasting Basilica Palladiana and temple-esque Teatro Olimpico – stand above the rest. Meanwhile La Rotonda is arguably the most perfect encapsulation of his ideas – and the identical design across all four faces has been copied around the world. See vicenzae.org.

Wanaka

Big ticket neighbour: Queenstown, New Zealand

Much more laid back than adrenaline junkie-packed Queenstown, Wanaka has several fabulous walking trails on its doorstep, its own highly picturesque lake and a vineyard on the outskirts. Kids and big kids should love the mazes and trickery of Stuart Landsborough's Puzzling World, and the Mount Aspiring National Park is just on the doorstep. See lakewanaka.co.nz.

See: The 20 must-do highlights of Wanaka

Playa Del Carmen

Big ticket neighbour: Cancun, Mexico

While Cancun is all gigantic all-inclusive resorts and cavernous nightclubs, Playa Del Carmen plays it considerably cooler, with a vibe that's far closer to the French Riviera or Ibiza's non-glowsticks side. The world class beaches are there, too, while there are also a prodigious number of language schools, full of sprightly young things learning Spanish by day and learning about the potent powers of tequila at night. See playadelcarmen.com.

Pretoria

Big ticket neighbour: Johannesburg

All jacarandas and graceful government buildings, Pretoria does a fine job of preserving its heritage. Several gorgeous buildings congregate around Church Square, while a strong museum includes Paul Kruger's House – devoted to the Boer leader – the Museum of Natural History and the Correctional Services Museum. The latter is at the Pretoria Central Prison, where political prisoners were once held and executed. It doesn't flinch from the gory truth. See tshwanetourism.com.

Rotterdam

Big ticket neighbour: Amsterdam

Defiantly modern Rotterdam is an experimental hub of all things modern architecture, with big, daring new projects being unveiled on a regular basis. Piet Blom's tilting, cube shaped houses built around an overpass are a classic, while the bold, colourful new market hall is a more recent addition. Throughout the city, though, shiny, unusually-shaped glass towers compete for attention in a country that's otherwise defiantly low-lying. See en.rotterdam.info.

See: Why Rotterdam is one of Europe's best cities

Compiegne

Big ticket neighbour: Paris

Compiegne is horse-breeding country, and also home to one of France's most marvellous palaces. The sprawling Château de Compiègne was built for Louis XV, and acts as a less gaudy Versailles.

There's also plenty of history in Compiegne. A railway clearing on the outskirts of town was where the First World War ended, as Germany surrendered inside a train carriage. During World War II, Hitler insisted on bringing the same carriage back to the same spot for France's surrender. See compiegne-tourisme.fr.

Potsdam

Big ticket neighbour: Berlin

A world away from Berlin's urban cool, Potsdam harks back to the era of Prussian might, with grand parks and palaces. The Sanssouci Palace, Orangery Palace and New Palace compete for grandeur, the Roman-style baths give an insight into how the Prussian higher orders kicked back and enjoyed themselves, while the giant Babelsburg film studio is a high temple of European movie-making. See potsdam-tourism.com.

Girona

Big ticket neighbour: Barcelona

A hugely photo-friendly city built higgledy-piggledy on the banks of the Onyar river, Girona's has done a wonderful job of preserving its old buildings and quarters. Cathedrals, fortifications and Benedictine monasteries are amongst the individual attractions, but it's really one of those places is best tackled with aimless mooching, picking up the extensive Christian, Jewish and Muslim history on the way. See girona.cat/turisme/eng/

See: Eating at 'the best restaurant on the planet' in Girona

See also: The world's 10 most amazing lost cities