French Riviera

Welcome

Depends on what you want to see and do

You can start your research here:
https://www.ricksteves.com/europe/france/french-riviera

I would stay in Nice

See my reply to your Provence question.

Definitely not St. Tropez. It has no train station, so trips to see other places along the Riviera will require too much transportation time.

I don't know whether there's affordable accommodation available in Monaco, or whether you're up for luxury-level places. I've been reading the forum for over ten years and don't recall anyone ever mentioning having stayed in Monaco.

If you're interested in seeing some of the hill towns (Eze, St-Paul-de-Vence, etc.), it may help you to know that bus connections may be better from Nice--but that should be verified for your specific situation. I'd want to have a list of potential target destinations and research public-transportation options before making a final decision. If there's no time to do that, my default decision would be to stay in Nice. If you're interested in art museums, Nice is sort of the no-brainer, because it has so many, though there are individual good ones scattered all along the Riviera and in some of the hill towns (Leger in Biot and the Galerie Maeght in St-Paul-de-Vence, for example).

Repeating some points above....

You would only stay in St. Tropez if you intended to stay only in that region and its beaches (among the best in the area).

Monaco does attract people at the high end for grand hotels and shopping, but things are a bit more limited as it is so tiny. Nice is the best transport hub with plenty to do within the city itself, and a wide range of restaurants and accommodations within its central neighborhoods. Thus it is the default recommendation, with some of the best new hotels and restaurants there as well.. Cannes has a collection of very nice hotels and boutiques, but not as much culturally and tends to be expensive (if that is what you seek, Monaco is a better choice).. THe best feature is the ability to go out to the Lerin Islands easily. Restaurant-wise, it has lost its luster. Antibes and Villefranche-sur-Mer are alternative smaller cities and village, respectively.

I've been reading the forum for over ten years and don't recall anyone ever mentioning having stayed in Monaco.

I have

but it has been a few years, we usually stay a bit down the coast now, if I had the chance I'd do it again this winter. We love Monaco and surrounding.

The Rick Steves guide answers all these questions. I would say Nice is your best bet, Cannes is just a beach, and Monaco will be quite pricey.