Stay in Nice for starters. Book in a private or dorm room at the Hostel Meyerbeer Beach. Pack a lunch for your day-trip or pick up a tasty sandwich at a Monaco bakery for a mid-day picnic in the gardens.
Take the #100 bus from Nice to Monaco for only 1.50 Euro. Be sure to stamp your ticket in the machine! The sightseeing along the way is free. There is also train service for about 5 Euros round trip.
Walk up the hill to the Prince's Palace where American film star Grace Kelley lives out her real life fairytale . Visiting the state apartments would cost you 8 Euros, but the daily changing of the guard at 11:55 am and terrific views are free. The principality is small but steep. Take advantage of the public escalators and elevators.
Smell the 4,000 roses at the Princess Grace Botanical Garden as you settle down to picnic on a bench. Later visit the nearby St. Nicholas Cathedral (AKA Monaco Cathedral) where many of the Grimaldi royals and Grace Kelly are buried.
Pretend you're James Bond - without having to dress the part - and check out the elegant Monte Carlo casino in the famous Golden Square (Carré d'Or) where you can window shop some of the world's top luxury brands while waiting for the casino to open at 2 pm. You'll have to pay 10 Euros to get in the first tier of ornately decorated rooms and another 10 if you want to the more exclusive. You don't have to be a high roller to play the slots or put down a small wager at the roulette table.
Ogle the yachts around Port Hercule and imagine Formula One race cars zooming through the streets during the Monaco Grand Prix when viewing stands are set up in the Harbor area.
Stop by the Brasserie de Monaco near the harbor for happy hour (6 - 8 pm) to sample the local micro brew and have a burger or a salad. You can also tour the brewery Mon - Sat from 11 am to 8 pm for 10 Euros, which includes beer tasting and a pissaladière (onion tart served like a pizza). Later on in the evening, there are DJs, live music and partying until dawn. But like Cinderella, you're racing the clock. The last train back to Nice leaves a few minutes after 11 pm. The 24-minute ride will get you back in plenty of time to check out nightlife in town.