Start the day with a cafe creme and a croissant at the Cafe de Flore, just as Hemingway did before you. (Stand at the counter--it's cheaper.) In the great Parisian tradition, stroll along the Boulevard Saint-Germain to the Luxembourg garden. Nearby, stop at the rue de Medicis side of the garden to find Eric Valli's photo exhibit, "Himalaya, World's Crossroad" hanging on the iron gates. For lunch, grab a baguette sandwich (3.5 euros) and a chair next to the Luxembourg's central fountain. Hop a metro (1.30 euros) to Les Invalides, and wander around the spectacular sculpture gardens of the Rodin Museum. It's free, like all French national museums, on the first Sunday of each month. If you're sightseeing midweek, head to the European House of Photography, free on Wednesday evenings. The Parc Floral, near the Chateau de Vincennes metro stop, costs 1.5 euros to enter, but has free children's puppet shows most days at 3 and 4 p.m. Until the end of July, it's also the site of the Paris Jazz Festival, with weekend concerts from riffing greats like Herbie Hancock and Erik Truffaz. As darkness falls, head to La Villette's park near the Porte de Pantin metro stop where you can lie on the grass and watch a movie. Upcoming flicks: Stanley Kubrick's "2001: A Space Odyssey" and Steven Soderbergh's "Traffic." The films are free, but if you feel a bit chilly, you can rent a deck chair and a blanket for 6 euros. And that frisson you get from simply being in the City of Light. Free of charge.
Susan Sontag calls Berlin "the San Francisco of Central Europe," and the place certainly has a history of attracting the young, the bohemian--and the broke. A good launching pad for thrifty travelers: the four-star Crowne Plaza (9 euros 5 for a double, via hoteldiscount.com). Tour the sights on public bus No. 100, a yellow double-decker that goes past all the major monuments. (A transit fare of 2.1 euros is valid for two hours on any bus, train or public ferryboat.) Stop off at the Reichstag, Germany's Parliament, and head up to its rooftop glass dome for a 360-degree view of the city. Next, buy a day pass (6 euros) valid for all 24 state-owned museums. At Hamburger Bahnhof, formerly a train station, you can gaze at the pop art of Joseph Beuys and Andy Warhol, then go to the Pergamon for the fabled Prussian antiquities collection. For lunch, fortify yourself with a bratwurst, falafel or Turkish doner kebab for about 2.5 euros on any street corner. Cool off at the Cafe am Neuen See, a beer garden in the Tiergarten park, where you can nurse a draught hefeweizen (3.5 euros) and people-watch as long as you like. Then, snag one of the 8-euro "choir" seats to hear the legendary Berlin Philharmonic. If you have any energy left, dive into Berlin's nightlife--covers for clubs rarely exceed 10 euros, and a bottle of Beck's is 2.5 euros.
Stick close to the River Thames and you can get by on a poorhouse budget. Start in Trafalgar Square at the National Gallery (which, like most national museums in Britain, is free) with its stunning Botticellis, da Vincis and Holbeins. Move on to the National Portrait Gallery, where you can gaze upon British greats from Cromwell to Auden to Diana. Meander riverward, and cross over to the South Bank complex. The National Theatre offers standbys, and though smash-hit productions sell out swiftly, you can get cheap day seats (line up by 10 a.m.) and standing room. The National's Platform Performances are lectures or talks by actors, directors or writers, offered once or twice a week at lunchtime or late afternoon, ranging from [Pound sterling]2.50 to [Pound sterling]3.50. Grab a sandwich and a glass of Chardonnay, sip and listen. Continuing east along the river, you arrive at the Tate Modern (beware: special shows like "Matisse Picasso" will cost you). Stroll the galleries, then sit at one of its picture windows framing St. Paul's Cathedral. Farther east, at Shakespeare's Globe theater, you can watch a performance standing in the Groundlings section--just like the Elizabethan rabble used to--for a mere [Pound sterling]5. Take a bus home for 65 pence, and smugly contemplate your thrift and smarts.