Looking for a bargain in Europe this summer? Forget hotels, restaurants and most forms of entertainment - the costs of which are rising into the stratosphere with the dollar near its lows against the euro and still weak versus the pound. But there still remains one pretty good deal in most European cities: the relatively cheap, comprehensive public transit systems. They not only provide an efficient way to get around town, but also offer some interesting day-trip options for those who want to wander out of the city center. London The fiercely expensive British capital, where a short taxi ride could easily cost the equivalent of $50, offers the far-reaching Underground as an inexpensive and efficient alternative. Despite Londoners' grumbles about delays, the Tube generally keeps to its schedule and covers a wide swath of this sprawling city. You're rarely more than a five-minute walk from an Underground station in central London — though stations become sparser the farther out you go. Unfortunately, in part because the lines are so deep and the system generally lacks air-conditioning, trains can be extremely hot in summer. (Five years ago, the mayor of London offered a £100,000 prize to anyone who could suggest an effective cooling strategy. Thousands of ideas produced no solutions.) Bring water and avoid peak transit hours if you can. To save more money, buy the pay-as-you-go Oyster card, which stores value and provides discounts on each trip. Even if you are only taking one Tube trip, said Mark Smith, founder of seat61.com, a comprehensive site on trains, still buy an Oyster card for a deposit of £3.50 pounds (about $7 at $1.98 to the pound) and a £1.50 credit. Then, he suggests, return the card at the end of your trip to get back the deposit so your ride costs only £1.50. “Who says smart cards make things simpler?” Mr. Smith asked. Day out On the outer edges of the District Line, Richmond makes a perfect half-day trip. Over the course of a few hours, you can visit the the Marble Hill House, a sprawling villa along the Thames originally built for the mistress of King George II or Richmond's town center, a classic collection of tiny shops and homes squeezed side-by-side, and some pleasant pubs along the riverfront. The bottom line The Tube runs until about midnight on weeknights and around 12:30 a.m. on weekends. Single adult fares cost £4 for rides in Zones 1 through 6. Paris The Métro, which opened in 1900 with a train linking Porte de Vincennes and Porte Maillot, matches London for its size, ease of use and comprehensive coverage of both the city center and outlying neighborhoods. And despite the subway attendants' reputation as somewhat surly and unhelpful, I've found most of them are exceedingly friendly and well-versed in English. Moreover, because the Métro has considerable above-ground stretches, it can also be a tourist attraction itself — parts of Line Six, in particular, afford expansive views of the city as it travels from Nation to Charles de Gaulle Etoile, And architecture buffs may appreciate the ornate Art Nouveau entrances, designed by Hector Guimard, that mark many of the Métro stations. Day out Out Known mostly as a residential neighborhood, the 16th Arrondissement, near the end of Line 6, doesn't get much visitor traffic. But the residences are exactly the reason to go. The Passy neighborhood, in the area, is home to many in the city's upper class, and by just wandering you'll find Parisian mansions both old and new, including what once was the home of Balzac). And don't miss the Musée Guimet, an Asian art museum that contains a trove of finely detailed sculptures and bas-reliefs French explorers took from the area around Angkor Wat. The bottom line Like the London Underground, the Métro offers not only one-trip passes for 1.50 euros (about $2.40 at $1.58 to the euro) but also multiride passes, which start at 5.60 euros. But Sara Bostley, a member of the VirtualTourist.com advice network who focuses on France, said to skip the various passes and buy a package of 10 Métro tickets (a carnet), which you can share among your fellow passengers if you are traveling in a group. Barcelona Befitting a city that considers 10 p.m. time to start ordering appetizers, Barcelona's metro runs late — nonstop on Saturdays, 5 a.m. to 2 a.m. on Fridays and 5 a.m. to midnight all other days. Be prepared for rush-hour type crowds in the wee morning hours. Day out Though few people think of Barcelona as a beach, for the 1992 Olympics the city rebuilt its Olympic Port area. In a triumph of urban planning, Barcelona transformed the port into a kind of Riviera, packed with seafood and tapas joints serving up fresh fish, all overlooking tall palms and flashy yachts. The Olympic Port lies near the terminus of the L4 line; get off at the Ciutadella Vila Ol?mpica stop and walk to the port region. The bottom line Single metro tickets start at 1.30 euros, and a 10-trip pass, a better buy because it doesn't limit use to one or two days, starts at 7.20 euros. Berlin Berlin's subway, known as the U-Bahn, dates back over a century, but it has weathered its age far better than the Tube, and many parts still look shiny, almost new. Don't rush through the U-Bahn's stations; some are architectural achievements in their own right. At the Alexanderplatz station, wander through the long pedestrian arcade under the soaring glass walls, or stroll into the Wittenbergplatz station's entrance, designed by the modernist Swedish architect Alfred Grenander. The U-Bahn runs all night on Friday and Saturday on many lines and until around 12:30 a.m. all other nights. Across the city, the U-Bahn connects with the above-ground S-Bahn urban rail system. Day out Less than 20 miles from downtown Berlin on the S-Bahn, the town of Potsdam, though known for the 1945 conference, actually contains a wide range of Baroque gardens and palaces. Visit the Sanssouci Palace, a Versailles-like gem of endless long hallways and colonnades and meticulously landscaped gardens. Relax from your Sanssouci walking workout at Potsdam's Neuer Garten, home to more palaces and manicured greenery. The bottom line Adult single-ticket fares start at 2.10 euros (short-trip fares are slightly less), and a one-day pass for adults starts at 6.10 euros. Rome Rome's metro, known to locals as the Metropolitana, is hardly the model of efficiency. Trains often run late, and the transit system does not reach all parts of the city. (On a trip to Rome last winter, I waited for nearly half an hour for one train, sitting at a depot covered in graffiti and trash while bored Italians napped all around me.) As in London, bring plenty of water on the hot cars, and remember to validate your ticket at the station before you get on the train for the first time. The two main metro lines both start running at 5:30 a.m. daily; Line A ends at 10 p.m. daily, while Line B ends at 11:30 p.m. Sunday to Thursday and 1:30 a.m. Friday and Saturday nights. Day out Most tourists focus on the grand architecture of ancient Rome and the Renaissance, but to the south, near the end of Line B, you'll find another kind of architectural spectacle. There, in the EUR district planned under Mussolini, is one of the world's greatest concentrations of Fascist architecture. At sites like the Museum of Roman Civilization and other structures, you'll find the stark stone, giant open spaces and towering colonnades of the Fascist style, which tried to hark back to Rome's ancient glory but wound up looking just icy cold and brutal. The bottom line One thing the Metropolitana has going for it is that it's cheap: single-ride tickets cost 1 euro, and a one-day pass starts at 4 euros. – NYT __