Nice

Here's a fun and family-friendly itinerary for your 10 days in Nice with your 3-year-old daughter, considering your constraint of having a car and being able to travel within a 300 km radius:

Day 1: Arrival in Nice

• Arrive in Nice, settle into your accommodation
• Take a leisurely stroll along the Promenade des Anglais and enjoy the beautiful views of the Mediterranean Sea
• Have a relaxing dinner at a local restaurant

Day 2: Nice City Exploration

• Visit the Parc Phoenix, a botanical garden and zoo that your daughter will love
• Explore the Old Town (Vieux Nice) and visit the Cours Saleya Market for some local treats
• Enjoy a family-friendly dinner at a restaurant in the Old Town

Day 3: Monaco and Monte Carlo

• Drive to Monaco (about 20 km from Nice)
• Visit the Oceanographic Museum and the Prince's Palace
• Explore the luxurious Monte Carlo area and maybe try your luck at the famous Casino
• Drive back to Nice for the night

Day 4: Antibes and Juan-les-Pins

• Head to Antibes (about 20 km from Nice)
• Visit the Picasso Museum and stroll around the charming Old Town
• Relax on the sandy beaches of Juan-les-Pins
• Drive back to Nice in the evening

Day 5: Eze Village and Cap Ferrat

• Drive to Eze Village (about 10 km from Nice)
• Explore the medieval village and visit the exotic garden
• Drive to Cap Ferrat (about 15 km from Eze) and visit the Villa Ephrussi de Rothschild
• Return to Nice for the night

Day 6: Cannes

• Drive to Cannes (about 30 km from Nice)
• Spend the day at the beach or explore the city's famous Croisette promenade
• Visit the Museum of the Sea or take a boat trip to the nearby islands
• Return to Nice in the evening

Day 7: Grasse and Gourdon

• Drive to Grasse (about 40 km from Nice)
• Visit the International Perfume Museum and take a tour of a perfume factory
• Drive to Gourdon (about 15 km from Grasse) and enjoy the stunning views from this picturesque village
• Return to Nice for the night

Day 8: Saint-Paul-de-Vence and Vence

• Drive to Saint-Paul-de-Vence (about 20 km from Nice)
• Explore the art galleries and charming streets of this medieval village
• Visit the Matisse Chapel in Vence (about 10 km from Saint-Paul-de-Vence)
• Return to Nice for the night

Day 9: Nice Beach Day

• Spend a relaxing day at one of Nice's family-friendly beaches, such as Beau Rivage or Castel Plage
• Enjoy some water activities or simply relax by the sea
• Have a beachfront dinner to end the day

Day 10: Departure

• Depending on your flight time, you can enjoy a leisurely morning in Nice before heading to the airport for your departure

I hope this itinerary gives you a good mix of sightseeing, relaxation, and family-friendly activities during your stay in Nice! Let me know if you need any more suggestions or modifications.