Danish weather is changeable, so if you catch sunny weather, this is how best to take advantage of it.  This will be a full day, from morning to evening.  Lots of walking, but at your own pace, and there are plenty of places to sit down, relax and take it all in.  

Unless it's summertime, you'll want to dress for Denmark's on-and-off wet weather.  It's rarely stormy, the norm's being a heavy mist or drizzle.  And it can get chilly, though rarely bitter cold.  The best way to provide for the exigencies of Danish weather is hooded outerwear over a sweater.  And of course, good thick-soled walking shoes.

Copenhagen is a wonderful city for walking.  It's never overcrowded, never filled with tourists, so you always get a sense of the locals being themselves.  There is only one fly in the ointment.  Copenhagen is in the midst of expanding its underground Metro -- building a "Circle Line" similar to London's.  This project will benefit Copenhageners, and tourists, in the future.  During construction, however, many key places in town will be marred by the mess of construction.  This includes the Town Hall Square, on one end of the main walking street (Strøget), and Kongens Nytorv, on the other end, as well as various other squares around town.  Because of this, Copenhagen as a walking city won't be at its best for the next couple of years.  The solution?  Get out of town and sample one of Denmark's great beauties, the coastal route between Copenhagen and Elsinore.  This can be done by car, but the most efficient way is by train.

From Copenhagen Central Station, take the Coast Line (Kystbanen) to Elsinore (Helsingør).  Visit Kronbgorg Castle, the site of Hamlet, then the wonderful 15th-century Carmellte Priory and its St. Mary's church, with its beautiful chalk frescos and baroque organ, one of whose organists was Dieterich Buxtehude, the teacher of Bach.  Then, if you want, it's a short ferry ride over to Helsingborg, Sweden, and back.  Helsingborg is a pretty town, but not much going on.

Before noon, take the train back towards Copenhagen and stop at Humlebæk.  You can walk or take a taxi back up the coast road (Strandvejen) to the wonderful Louisiana art museum.  A little beyond Louisiana at the first crossroad is Gamle Humlebæk Kro, a delightful country inn, for lunch.  Afterwards, you can stroll back to Louisiana and walk off lunch, perusing works of the great 20th-century masters inside the converted manor house and outside in the sculpture garden, with a splendid view of the Sound and the island of Hven, where famed astronomer Tycho Brahe built two observatories. (Louisiana is closed Mondays.)

Then, mid-afternoon, walk or taxi back to Humlebæk and take the southbound train to Klampenborg.  Klampenborg is part of the "Whiskey Belt" of stately homes, including Hvidøre, the palace of the dowager empress of Russia, born a Danish princess, who fled the Russian Revolution.  The American ambassador's residence is also in Klampenborg.  You'll also see Bellevue, a major development of famed architect Arne Jacobsen.  Klampenborg borders an enormous park, Dyrehaven (Deer Park).  Take a horsedrawn carriage up to the king's hunting lodge, The Hermitage (Eremitagen).  Of course you'll probably see lots of deer along the way.

By now, if your timing is right, it will be getting late afternoon, which will make for a picturesque carriage ride back, though if it's summer, dusk won't arrive until late night.  Klampenborg not only has Denmark's most distinguished neighborhoods but Denmark's funkiest amusement park, Bakken.  Think Coney Island in the Hamptons.  It's Europe's second-oldest, after Tivoli.  There's no admission charge, and for that reason, you see the Danes-in-the-rough.  Its a favorite haunt of youths, with lots of beer drinking and carousing.  But it has a great roller coaster and old-fashioned midways, plus Bakkens Hvile, where a bevy of Denmark's well-ripened "red-hot mamas" sit around the stage and regale the audience with bawdy songs and dances.  Of course it's all in Danish, but you'll get the drift.

If you're hungry for dinner by then, try Restuarant Piil on the edge of Bakken, on a pretty pond, or, if you've booked a table ahead, there's The Red Cottage (Michelin starred) across and a little up Strandvejen.  If your hotel has a good concierge, maybe he can get you in. Otherwise, take the train back to Copenhagen, freshen up and go to Tivoli.  If you're going to eat at Tivoli, then Grøften is a good bet.  The other places are overpriced and a bit formal. Grøften is a little more reasonable, and it's the place to go in Tivoli for traditional Danish fare and ambiance.  Go for one of the "platters" with small samplings of different Danish favorites.  The later it is the more they let their hair down.  But it's good vibes.

If you're feeling like a Viking, your first course will be the marinated herring (sild) on Danish rye. (If you're really authentic, ask for "stegfedt" instead of butter to spread on the rye bread.)  Order a glass of ice-cold Aquavit (Danish snaps) -- "Red Aalborg" is always good -- and a glass of "Green" Tuborg or Carlsberg Hof on the side.  After your first mouthful of herring and rye, raise your glasses, say Skål (be sure to make eye contact with all the other skålers) and toss your snaps straight down, immediately chasing it with a gulp of beer.  Now, you don't have to do this every bite, but that's how you start off a traditional Danish meal.  The rest, again, depends on how much of a Viking you're feeling. 

The entertainments at Tivoli are a few rungs up from Bakken.  Besides a season of European and international headliners, Tivoli has one of the few remaining authentic commedia dell'arte theaters. Whether you dine there or not, Tivoli is a lovely way to end the day.  It's great for strolling, people-watching, or finding a bench in a little nook somewhere.

And that's your day in Denmark.  No tour buses, no crowd to follow, no hustles, no hassles.  You can start off mid-morning and end mid-evening. or adjust the length to suit yourself.  The main thing is, along the way you've seen Denmark from street level, first-hand and without being led around.  And most Danes speak English, so don't hesitate to ask if you need help.  Your roundtrip train ticket is good for the whole journey including stops. (In Klampenborg don't confuse your Coastal train with the S-trains, which are local metros and use different tracks.)  

Denmark has a vibrant culture, and the Danes have evolved a society and infrastructure that work. The more Denmark you get as a living experience, the more you understand why it has been recognized by a number of international surveys as the happiest place on earth.