When you visit a European city in summer it can be a bit of a scrum. Faced with queues that stretch several times round the Colosseum or a 20-deep crowd in front of the Mona Lisa, it’s all too tempting to give up the sightseeing and head to an alfresco cafe.

So, if your New Year’s Eve resolution is to get more out of your city break than a headache, the key is to visit in winter.

Take Madrid, for example. In summer it’s packed to the rafters and too hot to handle. Head there in the colder months and, not only can you get a foot in the door of the Prado, you won’t be just visiting for the air con. Here are a few things you won’t be too hot, bothered and crowded-out to do:

Learn from the masters
A must for art lovers is a visit to the Prado Museum, the Reina Sofía, the Thyssen-Bornemisza – or all three. They are within easy reach of each other but if you want to do any of them justice, you’ll need more than a day. The Prado is perhaps Madrid’s best-known attraction and has more than 7000 paintings, following the history of art from the 12th through to the 19th century. For something more modern head to the Reina Museum. Madrid’s leading modern art museum does a fine line in surrealism and its ‘Mona Lisa’ is Picasso’s Guernica.

Find your team spirit
While you might have trouble getting your hands on tickets to see Real Madrid at the Santiago Bernabéu stadium, you can still visit the stadium for the grand tour. For €9 you can get a panoramic stadium view, have a wee nose round the presidential box and changing rooms, and even walk down the players’ tunnel. You’ll also get access to the benches and coaching area, Bernabéu pitch, trophy room and club shop. It’s interesting even for those who think ‘offside’ refers to the bad bit of cheese, take my word for it.

Make like Hemingway
Whatever your opinion, there’s no denying bullfighting is part of Spain’s heritage. This is particularly evident in Madrid, which has the most important bullring in the world, according to Madrid’s tourism bureau. Las Ventas stages the hardest fights and attracts the best matadors (‘aficionados’) in front of a crowd capacity of 25,000.

If you don’t think you can witness the slaughter of six bulls in the name of entertainment (and I certainly couldn’t), you may find it easier to simply do a tour of the stadium and at least arm yourself with the knowledge to make an informed opinion.

For €5, you’ll learn all about the sport in which matadors are more highly regarded than Hollywood superstars, without having to see any actual gore.

Dance the night away
If there’s one thing that screams Spain from the top of its lungs, it’s flamenco. This passionate display of song, dance and music is said to have originated in Andalucía in the south of Spain, but it’s alive and kicking in Madrid.

There are loads of formal shows in concert halls that cater well for the tourists (the cost of the shows varies and sometimes you’ll get a free drink or meal as well) or you can do what the locals do and head to one of the numerous bars along Echegaray Street, or bar hop around Plaza Santa Ana. Don’t expect this to be an early night, though, as many performances don’t start until after 11pm.

Support the economy
If there’s one thing I like to judge a city on, it’s the quality of the shopping. The fact I came home with three pairs of shoes and didn’t pay more than €10 per pair says something: I really should have bought more.

Don’t miss the area between Puerta del Sol and Gran Via for high street chains, department stores and cheap shoe shops. If you can’t get enough of the shoes, stop by Augusto Figueroa street in the Cheuca district. It’s known for its designer shoes at good prices.

Amanda Tomlinson travelled to Madrid with Busabout (020-7950 1661; www.busabout.com. A hop-on hop-off Flexitrip pass round Europe, with six stops, is £259. A Western Loop tour, which takes in Madrid, is £299.