Driving into Las Vegas you can be forgiven for wondering exactly which city you've arrived in.

On one side the Eiffel Tower decorates the skyline, while elsewhere the Statue of Liberty looms proudly above neon-lit buildings. Then you catch a glimpse of what looks like St Mark's Square in Venice.

However, Europe is on the other side of the Atlantic, and New York is over 2,000 miles away. It's 20 years since I'd last visited Las Vegas, the neon-lit oasis of Nevada, USA, and I quickly realised it had changed beyond all recognition.

Huge country-themed hotels, with their smaller-scale replicas of famous landmarks, have sprung up as well as MGM Resorts International's 8.5 billion dollar CityCenter project.

For years the heart of Vegas must have been one big building site. But now much of the work is done - and the result is a stunning series of sweeping edifices.

We stayed in perhaps the swankiest building of the lot - the Aria. This vast, horseshoe-shaped resort hotel and casino has more than 4,000 rooms. When we arrived it was all a bit daunting. But the signage was good and when we reached our room we had a great view of the city.

The Aria is just one of MGM Resorts' new properties whose opening, happily for the city, co-incided with new air services between the UK and Vegas by British Airways and Virgin Atlantic.

On our first night we went to the Aria's 1,840-seat theatre to see the fabulous Zarkana show, the story of a magician in an abandoned theatre who has lost his love and his magic.

You can gamble away in Las Vegas but there are other things to do as well. We went to Siegfried & Roy's Secret Garden where lions and tigers were on view as well as playful dolphins.

Then there was a tour of the Shark Reef Aquarium at the Mandalay Bay hotel. This featured more than 2,000 creatures including a Komodo Dragon.

At the nearby Luxor hotel we saw a Titanic exhibition. This was really interesting. On show were more than 300 items recovered from the wreck of the ship on the Atlantic seabed.

If the Titanic display was not harrowing, the Bodies exhibition certainly was. Real cadavers and body parts are used to display the human body and all its functions. We were told that everything was real except for the eyes.

This exhibition may not be for everyone, but it is thought-provoking.

As we walked back to our hotel in warm, late-afternoon sunshine, hundreds were arriving in the city to escape plunging temperatures in other parts of the world.

The town needs the crowds. As the big buildings of the CityCenter project were rising, the economy was plunging. Things are still a little tricky, but Las Vegas still managed to welcome almost 40 million visitors in 2012, with hotel occupancy levels as high as 87.4%.

The need for the town to offer more than just gaming tables is reflected in figures for 2011, which showed that just 7% of visitors to the city came just for the gambling.

We had reached Vegas after a spell in southern California. Our first stop had been in Los Angeles' Beverly Hills district at the Beverly Hilton hotel.

We took a walk down Rodeo Drive, one of the plushest shopping streets in America. Brand-name shops - and high prices - abounded.

The weather was fabulous. It was January but there were no clouds at all. The temperature was around the mid-60s F and you could walk outside in T-shirts.

We took a tram tour of movie stars' homes. Most modern actors and actresses guard their privacy so what you see on the tour are the residences of the old-time stars.

With the weather continuing to do its stuff, we moved on to the coast at Santa Monica and Loews hotel.

Loews is right on the beach and we had a good view across the sand towards the town's pier. More than 100 years old, the pier effectively marks the end of arguably America's most famous highway - Route 66.

It was a Sunday and we joined hundreds hiking up and down the pier. Kids shrieked on a roller coaster while anglers tried their luck off the end of the pier.

After Santa Monica and Vegas we had driven around 260 miles to Palm Springs. We passed through some amazing countryside, wide-open desert fringed with mountains. Even in January the ground was dry.

One feature was the dead-straight roads. Sometimes you could see for 10 miles or more.

Palm Springs is another place sprinkled with movie stardust.

There was plenty of dust around as we arrived - so much so that high winds had whipped up dust clouds so dense that a number of roads into town had to be closed, including one leading to our hotel.

It was infuriating. We had driven for mile after mile across difficult terrain without a hitch, and now here we were, just a short hop from our hotel with no way of getting there.

Bizarrely, we were helped by a policeman and the man he had clearly just stopped for a traffic violation. Between them, cop and offender gave us a detour route so we finally reached our destination.

Our hotel - the Renaissance - was right in the heart of a town where planners have ensured that buildings are kept to a modest height. There are no high-rise blocks.

Palm Springs and the other desert resorts such as Indian Wells can have some seriously hot weather, with temperatures reaching 120F in August. January, though, is a great time to go and we had temperatures of around 71F during our stay.

The main streets of the town have a laid-back feel. There's a Spanish/Mexican atmosphere about the place, and attractions include a theatre and plenty of shops and restaurants.

It was the Frank Sinatra-led Rat Pack that put Palm Springs on the map and it has proved popular ever since.

One of the highlights of the year in these parts is January's Palm Springs International Film Festival founded by the late Sonny Bono of Sonny and Cher fame.

In early March the area hosts the Indian Wells professional men's tennis tournament - one of the most prestigious outside the Grand Slam events.

We sunbathed round the pool, yet we could see snow on the tops of the nearby mountains.

England, stuck in mid-winter cold and gloom, seemed a long way off.

Travel facts Peter Woodman travelled to the USA with long haul specialist Hayes and Jarvis and stayed two nights at the Beverly Hilton, two nights at Loews Santa Monica, two nights at the Renaissance Palm Springs, and four nights at Aria at CityCenter, Las Vegas. Departing on May 5, a 10-night Hayes and Jarvis package based on the same trip costs £1,399 pp based on two sharing, including room-only accommodation, Virgin Atlantic flights from London Heathrow and car hire. Regional departures also available from Glasgow and Manchester.