Crossing a border you will not notice
Monaco is a sovereign state. It is in Schengen and uses the euro, so there is no check and no formality — you will cross into France without realising it. It is not in the EU customs union, which matters for shopping and almost nothing else.
The train from Monaco-Monte-Carlo runs along the coast in both directions and reaches most of these in well under half an hour.
East: Menton and the border
Menton is the last town before Italy — pastel, warm, and famous for lemons, with a festival built around them in February. It is quieter and cheaper than anywhere on this stretch.
Roquebrune-Cap-Martin, between the two, has a medieval village above the sea and a coastal path.
West: Èze and Nice
Èze is a village perched on a rock high above the sea, with a cactus garden at the summit. The bus is the sensible way up; the footpath from the shore is a genuine climb.
Nice is twenty-odd minutes away and is a real city — a proper old town, markets, museums and a long public beach.
If Monaco feels expensive, everything on this list is the corrective.
Paris, far to the north, is a journey rather than a day out; its own visitor guide is My Paris Travel.
Chapelle Sainte-Dévote
Port Hercule
Larvotto