You may be dissapointed!
Unless your an F1 fan there is not much in Monaco, it is a crowded, congested hell hole with no parking and over inflated prices, however the coast is nice, this year we stayed on Menton (10 min ride from Monaco) which was very nice.
Why not check out the ride reports on this forum for more ideas, I have one from last year where we rode the Route Des Grand Alpes and stopped near Monaco
http://www.ukgser.com/forums/showthread.php?t=279972
And the year before I went to the Stelvio - again this is unlikely to be a high point of the trip, but the Journey there is fantastic and there are so many other great passes you can work into the trip.
http://www.ukgser.com/forums/showthread.php?t=247181
Get the Motorcycle Journey's book for more inspiration - 300+ passes covered in 75 trips - and most trips require a day.
They are not close together though, I think what escapes a lot of people is just how big the Alps are (The size of England, Scotland and Wales) - you would not try and see all of the UK in one trip, and then add in the fact 90% of the UK roads are pretty crap, yet 90% of Alpine roads are better than the best 10% of UK roads and you can see you need a few months to "Ride the Alps"
The South Coast (and Route Des Grand Alpes) and the Stelvio is not an easy combo unless you have a lot of time, or just blat between the two.
RDGA starts around Annecy - a long days Motorway ride from Clais (500+ miles) so assuming you have a bit of travel to the crossing is likely to require 2 days travel.
Route Des Grand Alpes (RDGA) to the Coast can be done in two days, but I personally prefer to spend a couple of nights here and there for a days riding about, otherwise you will be pitching camp almost every night.
So after four manic days of riding and making / breaking camp you can go and see what a dump Monaco is (luckily this will only take 15 minutes to establish and you can go back down the beach and have a well deserved break)
Now off to the Stelvio, 350 miles of main routes and boredom would get you there in a day if that's what you want, but I would suggest going back up the French Alps taking in some different passes - my suggestion would be to take 3 days...
Work back up towards Bourg St Maurice, over the Saint Bernard passes, then head towards Andermatt taking in the Furka (Ideally stop for an extra day to ride around the Tremola, Nufenen, Grimsel and Susten) now go over the Oberalp and run down to St Moritz taking either the Julier (a great flowing ride) Albula (Tighter, bumpier and prettier) or Fluella (half way between the other two and my choice) then the last little run to Bormio and the edge of the Stelvio (I would choose Livigno to stop at) This is 3 days riding, two days to get to Andermatt and another day to Livigno / Bormio
As a whistlestop tour you are now 7 days in, I would suggest 10 days would be better to allow an extra day in Andermatt and two in the French Alps. You still have to ride the Stelvio and get home (another 2 days of mainly motorway and 650 miles) I would rather ride up through Germany and the Black Forest (still do-able in 2 days) but would also bag an extra night here and ride the B500 (an easy one to tick off the list on your way home)
So you need a minimum 4 days in / out of the Alps, 2 days to reach the coast, 3 days to reach the Stelvio and a day each at Monaco / Stelvio making a hurried 9 day trip and only staying at the same campsite for a second night twice. I really would suggest a minimum of 10 nights for this journey (and more if you can spare them)
Riding abroad is easy, if you have ridden for a day in the UK the same thing applies, the biggest difference is speeds, French motorways are fast and deserted compared to the UK, but Alpine roads are slow - still deserted, but with far more corners per mile than even the twistiest of UK routes, many of the corners being 1st or 2nd gear and views you just want to keep stopping to photogaraph / enjoy.
Plan for 30 mph moving average on the mountain routes (your unlikely to average as much as 40 on moutain roads) which gives a fair days riding of 180 - 210 miles (Under 7 hours riding, plus food / photo / fuel stops) I reckon on 15 minutes stopped for every hour riding + an extra 30 minutes for lunch on a leisurely day (and why go on holiday to have stressed days)
Motorways are fast, at a legal 83mph (130kph = @90 on the GS speedo) you will average about 65-70 genuine miles per hour after fuel / toll stops so 500 miles in a day is possible (if a shade boring) but gets you where you want to be real quick)
Personally I would go for the South Coast, or the Stelvio, and plan on ten days otherwise you spend 50% of your holiday on Motorways - I can't say which is best as they are both unbelievably awesome, and you wil want to keep coming back so you can do the other one next time, then the Dolomites the time after, and then Austria and Salzburg