Rifugio Mario Bezzi – Gian Federico Benevolo
A full glacier equipment and skills are neaded to ascend the Gran Paradiso (4061 m).
An alternative is a Tresenta (3609 m) without the glacier and similar views.
Rifugio Vittorio Emanuele II & Gran Paradiso or Tresenta
Rifugio Federico Chabod
Rifugio Vittorio Sella
All huts accepted credit cards and offer piknik packages for the day, but mostly just sweet. Even the breakfasts are mostly just sweet.
Charging was accessible on all huts.
Most huts expects you to bring your own sleeping bag linen. Some offer renting it for around €5-6.
Half board overnight is around €50-55.
Huts are busy in the season. Booking more than month in advance might be necessary. Or you must be lucky.
No huts have online reservation. Asking for couple of dates and then finding confirming those free in a sequence among all might be handy.
No dogs allowed in the national park.
It takes 3 connections to get back to the car to Valgrisenche, so you must catch the bus in Cogne around 12:35.
There is no server searching all the public transport in the Italy (for the record: this observation is from 21st century and hopefully change in the next millenia).
We used rome2rio.com to discover transportation options, look for time tables on Google Maps, look for bus stops in mapy.cz and found what's missing by simple Googling the names or browsing sites of the given operator. None of that gives the full picture alone. Some don't find a connection if you search for a village right next to the station (e. g. Valgrisenche vs Bonne), some miss some connections etc. Time consuming.
In buses, credit cards are not accepted. Contrary, in central bus stations, they don't want to sell you the ticket even by cash and force you to find a central office and return with the ticket. Better do it in advance.
Alternatively, the taxi for around €110 can drive you back to the car. List of taxis by local tourist info.
Even more alternative way of getting to the car is to rent an e-bike in Aosta and getting back to return it before 16-17h.