With so many millionaires crammed into its 0.78 square miles, its awesome architecture, improbable number of spotlessly-lush parks and one of the smallest royals-to-commoners ratios in the world, you'd be forgiven for thinking Monaco is something dreamt up as a vehicle for a Grace Kelly film.

In fact, that was probably what was on François Grimaldi's mind when he seized the place in 1297. Either way, it's every bit the film set it always has been and one in which, for a day or two at least, we can grab a walk-on part.

And walking is the way to see this most elegant strip of the Côte d'Azur, with its mix of bustling streets, quiet lanes and floral parks separating its two great landmarks: the Prince's Palace and the casino at Monte Carlo.

Actually, make that strolling. That's what the locals do when they're not riding around in open-top Bentleys. It's not good to work up a sweat in chinos and Ralph Lauren.

This is not a place to be under-dressed, unless you want to seriously stand out. Being an extra here means making an extra effort if you want any chance of blending in.

The only concession worth making is shoes; ones that'll help you get up and down hills. Of which there are a lot.

A leisurely afternoon can take you from the palace at what is the gateway to the principality, to the casino in the ritzier and most famous of its seven districts, just across the spectacular drop to the harbour. And it's a similarly manageable stroll to get down to those yachts you can see below.

So, a word of comfort for those wondering whether one of those money belts will spoil the line of a nicely cut jacket: while the place may be ridiculously pompous (its 35,000 population even have a local dialect and national holiday), it is relatively safe. Plain-clothes police patrol the tourist spots and they're big on CCTV. Cameras are everywhere. It is a film set, remember.

So, a starting point. It's a steep slog from the centre of town up to the palace, but you've stunning views with every step before you reach the square on which is played another sign of pomp: the midday changing of the guard.

And if you're one of those that don't do palaces, take a tip and do this one. You get to see the Throne Room, the Palatine Chapel and, most importantly, the private apartments; all aided by audio guides in English which help you get a taste of the Grimaldi lifestyle as you soak up the Renaissance architecture of the courtyard.

Alongside are the spectacular St Martin Gardens and the cathedral which houses the tombs of Prince Rainier and Princess Grace. But it's the old-town feel of Monaco-Ville, with its narrow streets and leafy squares, that gives you the sense that you are somewhere special. It's worth stopping for lunch in one of the open-air cafes - and visiting the chocolate shop. It helps if you speak just a little French.

This is the area known as the Rock, the prominent headland from where the place is both ruled and governed. It's also the place to get lost and be a tourist. If you want to see and be seen, then it's time for that stroll downhill.

It's worth taking a detour along the winding and undulating alleyways that sit behind the main roads of La Condamine if you want a sense of how ordinary Monegasques live. You'll pass front doors and occasionally, be warned, reach a dead-end. But no one will mind you finding a short cut.

Everyone goes to the Café de Paris, which sits bang outside the casino and features a terrace from where you can watch the supercars lining up outside the casino or try to spot someone of note at a nearby table. Just don't expect decent service from waiters who make it clear they've enjoyed better clientele before harrying you out of your seat as soon as they spot an empty cup or a clean plate. The cafe does have its own free gambling area, ideal for low-rollers who prefer slot machines to roulette tables. But that cheapens the experience.

From any of the vantage points, Monaco appears a thriving hub of high rises, but there's a lot of greenery set in among all that concrete. And it's pleasingly green, thanks to all the trees and shrubbery that line the pavements.

But for the best of it, head for the Jardin Exotique.Be aware, you will need those walking shoes here. It's steep, built into the side of the rock, and distinctly South American with its array of cacti, which contrast well with the white statues, the red terracotta roof lines below and the sea beyond. There's even a cave full of stalactites to enjoy, with an equally ridiculous number of steps.

But away from the attractions, Monaco is a place where you can stroll all day and enjoy a surprising amount of peace and quiet away from the bustle. You'll even come across lifts here and there to help you onto different street levels.

And it's worth doing it at night, grabbing a vantage point from the harbour and looking up as the hillside seems to come alive, or taking a taxi into the mountains and pausing at a viewing lay-by. But if that sounds like too much hard work, there's an excellent open-topped hop-on, hop-off bus service that trundles around in a continual loop - a single ticket will last you two days.