In 3 words: Unusual and fun.
Monaco is usually a day-trip destination unless you plan to spend a lot of time and money in the Grand Casino.
Distances are walkable, but require a lot of climbing and descending, so you may want to consider public transport to conserve energy when moving between Old Monaco and Monte-Carlo.
Worthy attractions: Musée Océanographique; Palais du Prince [did not tour inside] and the daily changing of the guard; La Collection Automobiles de S.A.S. le Prince de Monaco; Saint Nicholas Cathedral; Grand CasinoJardin Exotique.
Left for another visit: Musée Naval; Musée des Timbres et des Monnaies; Jardin Animalier; Nouveau Musée National de Monaco – Villa Sauber.
Last visit: September 2022.

Despite the statement at the top of the page about it being an intraday destination, Monaco can easily sustain a couple of days of exploration, despite its well-known minuscule dimensions. We visited for good portions of two separate days two decades apart, and just scratched the surface. The tiny country is busy around the year, very clean, and very visually interesting.

Somewhat surprisingly, there are many small green oases and quite a few pedestrian enclaves. Both walking and driving can be very confusing, so a good map at hand is essential.

Old Monaco ♥ is a little jumble of narrow streets and the only part of the country where architecture is predominantly more than a few decades old. The Palais du Prince is not as imposing on the outside as many other rulers’ palaces and is open to visitors only for a few summer months when the prince is not in town. The daily changing of the guard ceremony ♥ is curious and slightly comical-looking.

The cathedral ♥ has a number of uncommon design features and feels like a museum with all the artifact descriptions. Chapelle de la Miséricorde ♥ is a smaller striking religious place.

Musée Océanographique ♥♥♥ is quite possibly the best marine life museum in the world. It can easily sustain half a day of exploring for those so inclined; the Polar Mission section is a delightful immersion for kids (in 2022).

By the marina halfway between the old town and Monte-Carlo, the Prince’s Car Collection ♥♥ – colloquially known as simply “La Collection” –  is quite impressive and very well executed.

It should be noted that both of the aforementioned museums have a lot of interactive information implements, from which I infer that other museums would offer a similar experience. There is a handful of other museums in town that may be worth visiting, including a Naval Museum, a Stamps and Coins collection, and a newish Museum of Modern Art.

Grand Casino in Monte-Carlo is usually a prime attraction; if you are not a gambler, you will likely still want to find yourself in front of it, if only for an Instagrammable shot. If you want to go inside and try your luck a bit, please remember to have your passport with you (required for entrance), dress up nicely (at least “business casual” – jackets for men), be ready to pay an entrance fee (€10 per person when we were there in 2002), and don’t expect a large variety of low-stakes games. The casino interior, in Belle Epoque style, may be worth the entry fee by itself for some.

The area around the casino is home to some of the most opulent hotels on the Riviera. They look the part, too.

Jardin Exotique ♥ sits on the mountain slopes and provides great views of the entire little country in addition to a great collection of different species of cacti and other tropical and subtropical plants. There is also a small museum of anthropology in the gardens and an underground grotto with regular guided tours (in 2002 offered only in French).

Other notes for France