On my three-day whirlwind tour of Rome, I learned some strategies that are worth applying to any truncated first visit to a major city: Call anyone you know who's on terms with the city, and take notes on their favorite restaurants, shops cafes. Borrow or buy the best guidebooksall the splendors are detailed in themand read up at home, on the plane, in your hotel room. And study a good map to get your bearings. Go for the obvious. In Rome, St. Peter's, the Colosseum, the ruins were the things I wanted to seethings I'd heard about all my life. Be flexible. Everything in Rome conspires to give you a sense of place, no street is without its treasures, so if you suddenly want to abandon sightseeing to an afternoon in a cafe, do it. Tip the concierge at your hotelor drop in at the local tourist officewhen you arrive, to secure reservations at heavily booked restaurants and learn the ever-shifting hours of Rome's museums and sites. (Everything is closed on Mondays.) A bus tour the first morning might be a good idea, to get a sense of the city and some idea of what you want to see. It's impossible to go to Rome these days without reflecting on the horrors of terrorism. On my TWA flight from New York, one that goes on to Athens, I asked a flight attendant who makes the trip regularly how he felt about the possible danger. His reply was, I think, a good one. Not only are the odds of being involved in an incident still very slim, he said, but airports and airlines have beefed up security. Moreover, he, for one, having been in love with Rome for half a lifetime, wasn't prepared to give up those pleasures to fear.

GETTING THERE: TWA, Pan Am and Alitalia all fly from Washington to Rome daily, via New York. Currrent fares range from $645 to $970 round trip, depending on the day of the week you travel and how far in advance the ticket is purchased.

GETTING AROUND: The best means of transportation in Rome is a great pair of walking shoes. But there is an extensive bus system that is fun to use, although it requires a bus map and persistence. There are yellow cabs, which are metered; but because there are various arcane surcharges added for certain destinations and at certain hours, if you're going any distance, fix a price with the driver (or get the hotel to do it before you start). Most of the luxury hotels have a car service to the airport, which costs about the same as a taxi.

GUIDEBOOKS: The best way to get a fix on the riches of Rome is to use a good guidebook and a good map. Some of the best guides ''The Blue Guide to Rome and Environs'' for hefty does of art and history; ''The Michelin Green Guide to Rome'' for detailed information onthe sights (it also provides three- and seven-day itineraries); and ''Fodor's Rome 1986,'' with compact and practical facts on everything from sightseeing to shopping. ''Rome and Villa,'' by Eleanor Clark, is not a guide but a great travel book that illuminates Rome as no other book does. If you can't actually get there, this is the next best substitute.

WHERE TO STAY: Rome has hundreds of hotels in every category, from deluxe to Pensione. Some of the best and most convenient include: Eden, at Via Ludovisi 49 (phone 474-3551), a block from the Via Veneto; old-fashioned, quiet, elegant, great views. Hassler-Villa Medici, Piazza Trinita dei Monti 6 (679-2651); impeccable service, beautiful rooms. Grant Hotel, Via Orland 3 (47-09; very grand, refined and elegant. Lord Byron, Via dei Notaris 5 (360-9451); small, smart and exclusive, a town house near the Villa Borghese. D'Inghilterra, Via Bocca.

WHERE TO EAT: You can get well everywhere in Rome, at the most formal of restaurants and at the simplest of trattorias. Some that come highly recommended: Papa Giovanni, Via dei Sediari 4 (656-5309); some think this is the best restaurant in Rome. El Toula Roma, Via de la Lupa 29/B (678-1196); very posh, expensive, with great, elaborate food. Andrea, Via Sardegna 28 (493-707); classic meals. Alfredo alla Scrofa, Via della Scrofa 104 (654-0163); the best of the famous Alfredo restaurants. Pino e Dino, Piazza di Montevecchio 22 (tel 656-1319); small and candle-lit, one of Rome's trendies. Piperno, Monte dei Cenci 9 (654-0629); located in old Rome's Jewish ghetto, it's great for summer dining outdoor. Quinzi e Gabrielli, Via delle Coppelle 5 (tel 659-389); great seaford and an oyster bar. Giovanni, Via Marche 64 (493-576); more wonderful Italian food. Ristorante Peppone, Via Emilia 60 (483-976); good for a big lunch. Dal Bolognese, Piazza del Popolo 1 (361-1426); next door to Bar Rosati, a favorite with film folk and artists.

SHOPPING: There are not real secrets about shopping in Rome. The best boutiques are located in the streets around the Piazza di Spagnathe Via del Babuino, Via Vittoria, Via Della Croce, Via Condotti, Via Borgognona, Via Frattini. All the famous name Italian boutiques are here, as well as some less well known (try Betrami, Via Condotti 19, for incredible displays of fantastic shoes). Clothes for men and women, linens, china, jewelry and leather goods are all available and, depending on the state of the dollar, you can save 30 percent to 50 percent on prices in the United States.