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While politicians agonise over the size of the Government’s debt, one of the most expensive publicly funded projects in recent years is quietly getting under way.

The 10 Best adventure playgrounds

No matter how chilly it is outside, come half term, you're going to need to tire out the children. Try one of these for size

Fort Niagara, Greater Niagara

Win your perfect New York State adventure

From the majestic mountains, cities and lakes to the pastoral farmlands and vineyards, New York State has it all and we are giving one lucky couple the chance to win their New York State Adventure of a lifetime!

<p>Gritti Palace San Marco</p>
<p>Roll out the red carpet: this grande dame returns on Friday, following a 15-month facelift. Built for the Doge of Venice in 1525, it acted as the Gritti family's official residence for years, before becoming a hotel in the 19th century. It's been a Starwood property since 1994, and its latest transformation features rococo sofas, Murano chandeliers and rich Rubelli textiles restored, with designer Donghia furniture and antique Girandole mirrors added to the lavish mix. Notable guests lend their names to the 21 suites – Hemingway and Guggenheim among them – while the Club del Doge restaurant flaunts tables beside the Grand Canal.</p>
<p>Gritti Palace, Santa Maria del Giglio, San Marco (00 39 041 296 1222; thegrittipalace.com). Doubles start at €485, with breakfast.</p>

The Big Six: Venetian palace hotels

Notable guests, romantic retreats and ultra-chic hideaways

Jubilation in Jordan: The top of the peak felt like the end-of-the-world - but what a view

The sign said, 'The end of the world'; as did the look on my three-year-old's face. Below us, the dusky pink desert canyons and dimpled, rocky mountains of the Jordan Valley stretched west towards Jerusalem. And somewhere, far, far below the precipice we'd scaled to 'Sacrifice View', a bright blue cap was now swirling away, whisked off my son's head by the sharp wind that greeted us at the summit.

The Shard's view is a new joy, but taking the high ground has always elevated the senses

Plus: A four-letter word arrives on Radio 4 and the latest spin on a misused word

<p>{1} Beer to Branscombe, Devon</p>
<p>This amble along the Jurassic Coast is perfect for dog-walkers. The South West Coast Path is canine-friendly and Branscombe and East Beach in Beer allow dogs on the sands. The Anchor Inn and the Mason's Arms, at the star and end of the route, are also recommended by DoggiePubs.org.uk.</p>
<p>5.3 miles, southwestcoastpath.com</p>

The 10 best coastal walks

Whether you want a short hike or more of a marathon, stretch your legs and enjoy some of Britain's best sea views

Errors and Omissions: When medicine and geology get mixed up in a purple haze

Our peerless pedant reviews the slips from this week's Independent

Feeling flush? Ticket prices fail to deter tourists as The Shard opening day sells-out

A visit to the top of the building costs £24.95 for adults and £18.95 for children

The massacre at Newtown has led to a heated debate about gun ownership in America

Newspaper's map of gun permit owners sparks backlash

On December 19, days after the horrific shooting at a Newtown, Connecticut, elementary school, President Barack Obama said he found it encouraging that a discussion had re-emerged about how to deter future mass shootings. "That conversation has to continue," he said.

Duchess of Cambridge to attend BBC's Sports Personality award show

The Duchess of Cambridge will attend the BBC's Sports Personality award show tonight in her first public engagement since leaving hospital for severe pregnancy sickness, St James' Palace said.

Open Jaw: Where readers write back

Southend to Newquay flights

Travel Challenge: A Brazilian break during Rio Carnival

Each week we invite three companies to offer us their best deal for a specific break. Today: Brazil for Rio Carnival. Prices are per person, based on two sharing, and include 10 nights' B&B, flights from Heathrow to Rio in February 2013, transfers and a one-day Sambadrome ticket.

<p>1. Church of St Peter and St Paul, Guildford, Surrey</p>
<p>23 December, free, 01483 202594</p>
<p>Wrap up warm to hear the carols in this ancient church. Mulled wine and mince pies should help to keep you toasty, though.</p>

The 10 Best carol services

From candlelit concerts to the famous King’s College Choir, we pick the best of this year’s celebrations of song

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