Milano to Cannes

What time of year is your trip?
What are your interests? (there are lots of places with art museums, for example)
Will you be driving or taking the train?
Are you interested in both sides of the border?
Are you trying to fill multiple days, or are you looking for one or two brief stops?

The closest town to Ventimiglia that I've visited is Menton, France. It has most definitely been discovered, but the historic center is very atmospheric if you can ignore your fellow tourists, of which there will be a great many. There are two interesting gardens, and Menton is said to be the warmest place on the French Riviera. That will not be a plus if yours is a mid-summer trip.

Thank you for the speedy reply. I will be renting a car and driving from Milano but plan to stay near Ventimeglio for a bout 4-5 days; We will be there March 8-17 so no sunbathing! I want to visit gardens, Roman ruins and vineyards! Travelling on a tight budget and don't know which I love better - France or Italy... i think we can't go wrong...

Noli is a charming town on the section of the Italian Riviera. It has a waterfront promenade, beach, medieval quarter, castle on a hill and a Michelin starred restaurant, Ristorante Il Vescovado.

The two Menton gardens I enjoyed were Val Rahmeh Botanical Garden (west of the center of town) and Maria Serena Garden (east of the center and not terribly far from Menton's second rail station). Neither is right in town, so I think driving and parking nearby will not be an issue--though I didn't do that. I should mention that both gardens are on hillsides and might be somewhat challenging to a person with mobility issues. My balance isn't as good as it might be, so I had to be careful.

I see that there is a third garden in Menton, Fontana Rosa, which I haven't seen.

Farther west there's a nice garden at the Villa Ephrussi de Rothschild on Cap-Ferrat. Parking looked like more of a challenge there. I assume there's useful information on the official website. The villa is interesting as well, but if you only care about the garden, the experience might seem pricey to you.

I believe there are a couple of gardens in Monaco--a botanical garden and a rose garden, but I haven't seen them, and I don't know anything about driving into the principality and parking there. I imagine the latter might come with a rather high price tag.

Traffic on the Riviera coastal road can get rather badly backed up, so there may be times when you'd do better to park the car and hop on the TER (regional train) that runs along the coast. Ticket prices do not vary, so you can make spur-of-the-moment decisions about that. Do watch out for pickpockets on and around the trains.

For me, Dolceacqua and Apricale are the best of the Ponente coast with Cervo not far behind. FWIW, Monet recommends Dolceacqua, too. For info: https://www.apathtolunch.com/2013/12/the-most-beautiful-villages-in-liguria.html

Remember that you will be there in March, a little early for most gardens and vineyards to be showing much. The Jardin Exotique in both Monaco and Eze le Village will be a good show - they are both mostly cactus and succulents. I wouldn't expect much from a rose garden in March.