For this trip, you can work out the daily sightseeing schedules on your own, depending on what best floats your artistic boat. Most cities have two-and-a-half days of sightseeing time budgeted, which should be enough to give the major museums a good once-over.

Head to London for Days 1 through 3. Your first order of business should definitely be the medieval, Renaissance, and baroque masterpieces of the National Gallery. The other great art collection is the Tate Gallery, now divided between two buildings, one on each side of the Thames; the original neoclassical gallery covers the British greats and the vast new space in Southwark, the Tate Modern, concentrates on international art in the 19th and 20th centuries (from Impressionism to contemporary works), with stellar temporary exhibits.

While at the National Gallery, you may also want to nip around the corner to stop in by the National Portrait Gallery (same building, different entrance). Although the collection exists more for the historical interest of its subjects, some artistically fine portraits reside here as well (especially by Holbein, Reynolds, and Warhol).

No museum buff should miss the Victoria & Albert Museum, which has London’s best sculpture collection (Donatello, Giambologna, and Bernini) and a fascinating exhibit on artistic fakes and forgeries, in addition to miles of decorative arts.

If you’re into Christopher Wren’s brand of Renaissance architecture, you’re in luck — the city’s full of it — but his greatest hit is St. Paul’s Cathedral. And I can’t imagine a trip to London without calling on the British Museum, at least briefly, where you can get the best overview of the ancient world’s art forms (Greek, Roman, Egyptian, Assyrian, Asian, Indian, and Islamic).

On the morning of Day 4, catch a Eurostar train to Paris. Spend Days 4 through 6 in the City of Light, exploring the treasures of the Louvre over a full day at least. Fans of Impressionism and French art in general should devote at least two-thirds of a day to the Musée d’Orsay. Paris has so many smaller art museums that choosing from among them can be difficult and squeezing them all in can be nearly impossible. Whole museums are devoted to single artists (Rodin, Picasso, Delacroix, Le Corbusier, and Dalí), and others are devoted to eras — such as the medieval at underrated Thermes de Cluny, or the modern at the incomparable Georges Pompidou.

Two of my favorite, slightly lesser-known art treasures are the Delacroix murals in the church of St-Suplice and Monet’s 360-degree Waterlilies in specially built basement rooms of the Orangerie, off Place de la Concorde. At the end of Day 6, hop on the overnight train to Florence.

Days 7 through 9 are for Florence. Reserve one entire day for the Uffizi galleries, a living textbook of Renaissance development. The Pitti Palace’s Galleria Palantina covers the High Renaissance and baroque eras thoroughly. Michelangelo’s David and his unfinished Slaves in the Accademia are a must, and Donatello reigns supreme at the Bargello sculpture museum.

Fra’ Angelico frescoed his brothers’ cells at his monastery of San Marco, and they’re now open as a fine museum of his works. Florence’s churches are so richly decorated I scarcely know where to begin: Giotto in Santa Croce; Ghirlandaio in Santa Maria Novella and Stana Trìnita; Donatello and Michelangelo at San Lorenzo and again in the Museo dell’Opera dell Duomo; Masaccio in Santa Maria della Carmine (the restored St. Peter’s frescoes by him and teacher Masolino) and in Santa Maria Novella (his Trinità fresco is the first work in history using true linear perspective). Then you can see Brunelleschi’s architecture, from the Duomo’s dome to Santo Spirito to the Pazzi chapel at Santa Croce. Florence is one place where you’ll definitely run out of time long before you run out of art.

Days 10 through 12 find you in Rome. Take the morning train here from Florence on Day 10 and start exploring the baroque period with Bernini’s sculptures on Piazza Navona, Piazza Barberini, and in the Galleria Borghese.

The Vatican Museums (home to the Raphael Rooms, the Pinacoteca painting gallery, and Michelangelo’s Sistine Chapel) take at least twothirds of a day. The Capitoline Museums split their collections between ancient sculpture and mosaics and Renaissance and baroque painting. Some smaller museums include the Doria Pamphilij collections and the Galleria Nazionale d’Arte Antica, split between the Palazzo Barberini (near Via Veneto) and Palazzo Corsini (in Trastevere).

Rome’s churches are blanketed with art, from Filippino Lippi’s frescoes in Santa Maria Sopra Minerva (where you also find Michelangelo’s Risen Christ) to the Caravaggios in Santa Maria del Popolo and Michelangelo’s Moses in San Pietro in Vincoli. Again, you’re unlikely to run out of art to ogle in just three days here.

On the evening of Day 12, get on the overnight train for the long haul to Barcelona. If you don’t like those overnight trains, wait until morning and hop the 8:55 a.m. train. Volareweb.com (http://buy.volareweb.com) sells no-frills flights to Barcelona for around $65.

Spend Day 13 in the Catalonian capital of Barcelona. You should definitely take in the intriguing early Picasso works at the museum dedicated to this hometown hero and make a survey of Antoni Gaudí’s whimsical architecture. At the end of the day, hop the overnight train to Madrid.

Plunge into the myriad museums of Madrid on Days 14 and 15. Spain is the land of Picasso, Velázquez, Goya, El Greco (by adoption), Murillo, and Ribera. You have a day to devote to the Museo del Prado and another day to split between the Reina Sofía museum (home of Picasso’s Guernica), the Thyssen-Bornemisza Museum, and — if you can stand any more art at this point — the Museo Làzaro Galdiano.

Day 16 is your travel-home day.