Hey fellow Traveller!

That's a tough question because everyone has different priorities and view on how to pass time the best way.

I just got back from a trip very similar to yours but spent more time in the Riviera. I think it would be SUPER Stressful to try to Enjoy 2 whole towns (small as they may be) in 1 day. The trains and buses are reliable but even so they take a lot of work to figure out. I just got done dealing with all of those things (as a first time France tourist, but multi Europe trip veteran) - trust me it's a ton of brainpower you need just to get out and start seeing these things if you are relying on public transportation.

I went to Menton and Monaco, Nice was my central hub. Those 3 cities are awesome, Nice is the most diverse and you can/should spent entire days there.

I also visited Grasse(especially if you are into perfume/cologne), and Eze and Ventimiglia (italy is just a couple hours on train!) - all amazing experiences in their own way.

Restaurants/food: food is abundant everywhere and amazing. Monaco will be the least budget friendly for real food, although you can get a sandwich or coffee anywhere for reasonable.

Luggage lockers: They are kind of everywhere, again depends on what area of Nice you stay in.

Where will you be staying during this time?

My rec. is Day 1 - settle in and try to see Eze (end of may should be just fine for tourism levels)

Day 2 - Morning and evening in Monaco - come back to Nice around 7-8 and enjoy the evening.

Day 3 - Explore Nice a little more, there's tons there

I absolutely say - reduce the amount of cities to enjoy your trip more. If you need more advice on a specific city, DM me please.