This might help people visualize the options
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A. From Menton to Tinee
The only notable pass is Col di Turini, good food / drink options at the top.
B From Tinee to Barcelonnette
There are a lot of other alternate routes here and that is why we always spend an extra night or two in the area (Barcelonnette / Valberg / Tinee) as there is just so much great and varied riding, just one extra day will allow you to loop around most the stuff you will miss by just choosing one route option.
1. The Modern Official route over La Bonnette - short and easy (plus "Bags" you the highest paved road in the Alps and is a great ride with stunning views at top (but no facilities,plenty on the approach and after the descent)
2/3. The original route over Couillole (Just before Valberg) Valberg (2) and Cayolle (3) - A bit more varied, Couillole is stunning, narrow and rugged, Valberg a real good ride on any bike with great curves and Cayolle is scenic and rugged again (Valberg is a handy place to stop for coffee or lunch)
4/5. After Valberg you can dive down Gorge du Daluis (4) and then over Col du Allos (5) - This ticks of more passes (and a gorge) than the other options and if your not bothered about following the "official" routes is probably the best for cramming as much into your ride as possible (as well as Valberg for Lunch there is a great refuge at the top of the Allos)
6/8/11. At Tinee head over Lombard (6) and then take Larche (8) - Many will say the most boring, and TBH I would advise taking La Bonnette, this is an option if you have done that before and want an easy alternative, the Lombard is a load of (wide and well surfaced) hairpins up and a very scenic run back down the other side. The Larche isnice enough, it is an easy pass but does have some nice curves and a handy little cafe by a small lake just before the French border.
6/7/9/10. Over Lombard (6) Colli di Valcavera (7) Sampeyre (8) and then Agnel 10, although this bypasses the options of 11 / 12 - For those that like a bit of rough, after the Lombarde yuo have aa bit of dull road before swinging up towards Sampeyre, this is a remote valley where you wind up and down some narrow roads, there is a small hostel that does drinks and snacks about half way along (and is very cheap) but not much else, going up Sampeyre (Heading North) is not so bad, but the descent into the town of Sampeyre is pretty rough, broken up and bumpy - great fun IMO, but any mates on sportsbikes or huge tourers may not be too happy. The you have Col Agnel that is a real Beauty, generally decent surface and wide and great views at the top.
C. Barcelonette to Briancon
I can only see one choice here - Col de Vars (11) the other route is predominantly main roads, you do get to ride past a big lake, but unless the Vars is closed or weather appaling I would take the Vars as it is a great riders road, wide, grippy, open, smooth.
Either way you still get to ride the Jewel in the Crown, the Izoard, one of my favourite passes int he Alps, not sure why as nothing is all that exceptional - except the gold rock formations, but I always love riding this pass.
D. Briancon to Bourg St Maurice
Three good options here, the classic route of the Galibier (14) is what I would do on a first trip, and it is fantastic, there is a small tunnel at the top so dodge that to go right over the highest point (or stop at the cafe just there and enjoy a cuppa whilst taking in one of the best views from the pass)
The second option would not be my first choice (15) it uses a lot of more main roads but there are a few variations and you could take in Alpe d'Huez and col du Glandon, and take a detour around Col du la Croix de Fer and Col du Mollard.
My second choice (or maybe first if you have done the Galibier before) would be to go over Col du Mont Cenis (good choice of restaurants at the top) this is also a bit faster and cuts out a bit of boring stuff between Briancon and Galibier and between the end of Galibier (Or the Telegraph to be precise) and Mondane - at the expense of a short stretch of motorway.
Hope that helps some folk decide they need a couple of extra days and don't forget to save a day for the 7 pass loop around Mont Blanc, you can stop anywhere between Bourg and Morzine to ride this loop.