Bus 100 (Nice - Monaco - Menton) is a very good option and costs a mere 1.50 € ( 2015 ).
It runs every 15 minutes mostly, and the trip takes 30-45 minutes.
It takes an absolutely scenic route along the coast, passing through seaside towns such as Villefranche and Beaulieu .
(There's also express bus 100X which takes the motorway and costs 4 € (2012); obviously not as good for sightseeing.)
In Nice, the 100 now leaves from Le Port ; follow link for exact locations on map.
(The departure stop has changed a couple of times in recent years, having previously been Ségurane , next to Place Garibaldi, and Promenades des Arts .)
Arriving in Monaco, there are 6 stops to choose from (do get off at one of these as the bus continues towards Menton):
Cimetière, Place d'Armes , Stade Nautique, Office de Tourisme, Place des Moulins, Les Carabiniers.
Heading from Monaco towards Nice, the route is slightly different; then the Monaco stops are: Les Carabiniers, Place des Moulins, Casino (Allée Lumière), Sainte Dévote, Place d'Armes , Cimetière.
The buses don't run very late :
last one from Nice leaves at 20:00, and from Monaco at 20:22.
First departures in the morning are about 6:00.
You'll find details and full list of stops in bus 100 timetable .
Alternatively, take the train ("Nice Ville" to "Monaco Monte Carlo").
It is faster (22 mins) and arguably easier, but costs a little more at 3.90 € .
There are about 2 regional trains per hour (daytime), according to SNCF .
A good thing is that the trains run much later ; last one leaves from Nice 22:25 and from Monaco 23:12 (on weekdays).
The above applies to regional trains (TER) which would probably be your primary choice on this route, though you could also catch an intercity/TGV.
travel.stackexchange.com/users/583/Jonik
I have just returned from Nice/Monte.
Great trip and good advice given here.
As of Nov 31 2013 the bus costs €1.50 each way and starts just off Garibaldi Square, pay cash.
Also, the Nice day pass has changed.
It is a 24 hour pass that costs €5 and can be used on all trams and buses in Nice except buses 98 and 99.
What does this mean?
The only bus that the pass covers that goes to and from the airport is the number 23 (catch it outside the Rail Station), takes 30-40 minutes to Terminal 1.
From there use the free airport shuttle bus to get to T2.
You ask, what about the 98 and 99 buses?
Well they now cost €6 each way
- the benefit is it is an express bus.
travel.stackexchange.com/users/9317/waney
We returned from the Cannes-Nice-Monaco Trip in May 2014, and the answers given above have helped us.
Although the starting point of Bus 100 has changed as rightly pointed out in answer by Ger : The 100 bus to Monaco now leaves from the Promenades des Arts stop outside the Musée d'Art Moderne/Contemporain near the corner of Av.
St. Sebastian and Traverse Garabaldi.
Here are some of the Bus timetables that I got as of May 2014.
And here are some timetables if someone willing to do the trip to Cannes.
In Nice, take Bus 200 from "Le Meridian" ,I guess near to McDonalds.
Bus 200 To Cannes And Return
And the Price List
travel.stackexchange.com/users/13769/TheAshwaniK
I have just returned from Nice, Easter 2014.
The 100 bus to Monaco now leaves from the Promenades des Arts stop outside the Musée d'Art Moderne/Contemporain near the corner of Av.
St. Sebastian and Traverse Garabaldi.
On arriving in Monaco we got off at Places D'Armes and walked up the pedestrian hill to the Prince Palace, then around to the Cathedral and past the Musée Oceanographique.
To the east of the Oceanographic museum, there are steps down through the gardens leading to the port where you can get a Bateau bus across to the other side to get to Monte Carlo and the Casino.
There's a short walk into the tunnel turning right off the port and you'll find an elevator around the corner to get up to the roadside on the southern end of the Hotel de Paris.
travel.stackexchange.com/users/13174/Ger
I just returned from doing this day trip as well, great advice here!
So as of January 2014, nothing has changed.
The new bus stop to get the 100 is at the southeast corner of Garibaldi Square (or Place Garibaldi in French) on Rue Catherine Segurane.
The best stop to get off and back on the 100 in Monaco is Places D'Armes.
It's right next to the Place du Palais, and the Prince of Monaco Car Collection, Aka Top Car Collection.
They have a dozen F1 race cars on display, and a myriad of cars from classic Ferrari's, Lamborghini's, BMW, to very old rare cars dating back to 1911.
They even have some horse drawn buggies!
There are no return tickets,
one way only, 1.50 each way.
Great little day trip, highly recommend it!
travel.stackexchange.com/users/10143/Paulie
A couple of days ago I compiled all the practical transportation options for a Nice to Monaco trip .
I though you guys might like to see all the possibilities, costs and advantages of each option.
As I grew up in Monaco, I have tested all the possibilities for you, from the bus to the bike trip... SUMMARY of the information available on the link .
Nice Downtown to Monaco – Bus line 100 (up-to-date-timetable)
Nice airport To Monaco - Bus line 110
(up-to-date-timetable)
Nice To Monaco by train (up-to-date-timetable)
Nice To Monaco by Taxi (with price estimation and rules)
Nice To Monaco by car with 4 options The Highway
: Take the Highway “A8”
The "Basse Corniche" (Low Coast-Road)
The "Moyenne Corniche" (Middle Coast-Road)
The "Grande Corniche" (Great Coast-Road) Nice to Monaco Ridding a bicycle
travel.stackexchange.com/users/19045/Monaco Addict
What's the  simplest and cheapest way  to get from central Nice, France to Monaco by public transportation?
How to get from Nice to Monaco by public transport?
travel.stackexchange.com
<public-transport><france><monaco><nice><french-riviera>
travel.stackexchange.com/questions/11066
travel.stackexchange.com/users/583/Jonik
Bus 100  (Nice - Monaco - Menton) is a mere 1.50 €, or the express bus 100X takes the motorway and costs 4 €. Alternatively, take the  train  ("Nice Ville" to "Monaco Monte Carlo"). It is posible to travel from Nice to Monaco by bus or train.
There are two types of bus from Nice to Monaco: Bus 100 and the express bus. The train runs from Nice to Monaco.