''Too much is not enough,'' proclaims the sign above the Cyber Cafe in Times Square, New York City. Next to it is Hansen's shiny new Brewery Restaurant, with its own on-site brewery. The area is all new, scrubbed, upmarket. It is a sign of the clean-up that is starting here and moving through the city.

The US Armed Forces recruiting centre is still in place - a single-storey kind of hut in the middle of the skyscrapers. But that and Hotalings Foreign News, where you can get all the British papers, are about all that remain of the old Times Square and 42nd Street district. The last time I was there, the future of 42nd Street west of Broadway was being discussed by the City Council and reported on TV. As a backdrop to the newscast the TV station sent a cameraman to video the street. It caught a live mugging in full swing.

Now the drug dens, sleazy cinemas and peep shows are all closed. Some of them have spilled round the corner to 8th Avenue, but it is a transformation amazing to behold.

Unarmed ''Times Square Improvement Area'' guards patrol in a friendly way; NYPD mounted police sit high on their horses scanning the scene up to the next mountie. They can quickly summon one of the constantly-patrolling police cars if trouble looms.

Murder is down by half in the last five years, and lesser crime is down by even more.

Harlem has kept up with and has even led the charge. Tourists now flock there, walking freely about, and the Japanese patronise it in their customary coachloads.

The Bronx is the latest of the NYC boroughs to change a 50-year-old way of life which has become accepted as if it were eternal. It was a Jewish area until the late forties and early fifties, when they moved out to smarter suburbs and were replaced by incomers made up of the poorest blacks and the new wave of poor Hispanics from Latin America - mainly Puerto Rico.

Anyone who is under 60 today will remember it by repute as an land of armed gangs, ridden by crime, from petty muggings to organised arson, drug dealing and gang killings. No-one from outside would go there if they could avoid it, except on baseball days to visit Yankee Stadium along heavily policed streets. I remember from before, that sometimes when the mid-town tunnel was closed or the traffic was bad, taxis would go from JFK to Manhattan cutting through the Bronx. The cabbie would apologise, close the windows and lock the doors.

Now the silent citizens are finding voices which say what is always true, that the huge majority want to go to church, to college, to work and to play in peace.

One of these voices is the Bronx Tourism Council which is articulating and promoting what has always been there - old time America, not just the Yankees, but the zoo, Fordham University, the NY Botanical Gardens and a dozen parks, one bigger than Central Park.

It has low-rise tenements with fire escapes at the front, and family-run restaurants serving old-style grits, pastrami on bagels, tuna melts on rye and more recent arrivals such as Burritos with salsa.

I made a sortie from mid-town Manhattan. ''Take the D-train,'' sounded more like a movie title, but was actually the directions for taking the subway from 6th Avenue at 47th. The subway was silver, clean, quick and smooth and was no more threatening than the London tube. It took about 30 minutes to get from 47th to 161st Street and Yankee Stadium, and a few more minutes to reach Fordham Road, the new ''Little Italy''. It cost $1.50. A cab would have cost $30 and taken longer. The D-train goes as far as the Botanical Gardens, the 2-train branches to the zoo and the 4-train goes to Woodlawn Cemetery where you can see the grave of Duke Ellington, if you are that way inclined, and passes the area where Edgar Allen Poe's cottage is to be found.

The Fordham Road underground station needs the attention of the clean-up movement, it being so unrepresentative of what is to follow. Two of the shortest, fattest, ugliest cops I ever saw, lounged against a wall with their hands in their pockets in a dark corner of the crumbling building. Outside it gets better. While it may not be as mild as a Cotswold village, it is no wilder than a busy city High Street in the UK.

Some of the features of its previous life remain, such as the gas station where you pay in advance in case you are a ''runner'', and where the attendant takes your money from inside a bullet-proof glass booth. Features like these are redundant now to the point of being quaint. Maybe they will be preserved for posterity.

The shopping streets are bursting with life, teeming with people along the sidewalks. The shops are ablaze with blindingly bright lights and the disco music blares out onto the street. Gracious it is not. No smart shopping malls here; but old-style stores packed with homely people and throbbing with life. There is a ''we're all in this together'' kind of warmth.

The side streets have one, two and three-storey brown or red brick houses which, as they get cleaned up and painted, look like you would see in an American movie of the fifties, and some have the style and charm of Edward Hopper paintings.

Eastwards lies Fordham University and south from this runs Arthur Avenue, the centre of Little Italy. It is quiet, low rise, charming, homely. There seem to be no national chains; everything is family run from the laundry to the deli and, especially, the restaurants. These are striving upwards towards a reputation for fine dining.

The Bronx Tourism Council speaks with a force which puts doubt to flight, and they feature their ''Visitors Fun Guide'' on the Internet, and promote the borough's opera company and symphony orchestra.

They are reviving interest in the history of the district, starting in the 1600s with the Swedish sea captain Jonas Bronck who owned it as farmland. But the biscuit is taken by its most famous son of all - Leon Trotsky, yes that Leon Trotsky. The local Bronx Home Times of 1917 proclaimed: ''Local man leads Russian revolution''. Follow that.