I need trip info planning for an interconnect alps trip.

I think 2 or 3 weeks is too much for all countries

Are you going to rent a car?

I would concentrate on maybe two close countries like switzerland and austria.

here is link for hostels in switzerland
http://www.swissbackpacker.ch/

My tip:

Fly to Geneva in Switzerland and start your trip there. It's only about 30-90 Minutes by car to great places in canton Wallis/Switzerland (maybe Verbier, Zermatt, Saas Fee, Portes du soleil). There you can ski in two countries on the same day (e.g. Zermatt = Switzerland/Italy, Portes du soleil = Switzerland = France).
From Geneva all three countries are reachable in a very short time. At this border triangle one side of the mountain is a country, the opposite side of the mountain is another country.
But I think in the mountains it doesn't matter, if you are in Switzerland, Italy or France, it's almost the same.
I think Switzerland may be the most expensive place, but the villages are nicer and more cultivated, maybe the best country of these three to finish your holiday with a little bit relaxing.
Enjoy your trip!

Fly into Geneva.

Rent a car and head up to Avoriaz for a couple of days to warm up in good snow and good parks. Avoriaz links to 12 resorts in France and Switzerland so reserve at least 4 or 5 days for this. After that ride 1 day at Les Grands Montets (Chamonix) and return the car to Geneva.

From there take the train to Saas-Fee, ride 2 days, then switch to Zermatt which is next door, ride 3 days. From Zermatt u can ski deep into Italy (Cervinia, Valtournenche).

From Zermatt take the glacier express to Chur. It's expensive but this train will blow your mind. If u want, make a 1 day stop in Andermatt. From Chur go up to Laax and then Davos. Reserve plenty of days for Laax.

From Chur it's an easy train connection to Austria (Tirol), take a train to St. Anton. End up in Innsbruck where you ride Nordpark and from Innsbruck you fly back home.

This way u get the best regions of the alps (Haute-Savoie, Wallis/Valais, Graubunden and Tirol). Switzerland and Austria have excellent train connections, its part of the lifestyle so use it...

This plan sounds good, but I think that would be too much of a hassle for 2 or 3 weeks

the plan von michael_bc is really good. another posibilitie is going deeper into france to ride the resorts of val d´isere and/or 3 vallee. 3 vallee with courchevel/meribel/val thorens is the biggest resort in the world. you cant ski all the slopes in a couple of days. so, you have a lot of slopes and backcountry to ski!
for the last 6 years me and my friends made such road trips in the alps. we have skied a lot but we havent tested all. so, theres always a reason to come back!
for me best time in the alps is march.
big airports near the alps are geneve in france, zürich in switzerland, innsbruck and salzburg in austria, mailand in italie.
so, nice days in europe!

@ markus:
Did you ever look into an atlas? ;-)

Geneva is surely not in France...

WRONG.
stop spreading bullshit.

Les 3 Vallees = 10 000 hectares
Tignes-Val d'Isere = 11 000 hectares
Paradiski = 14 000 hectares
Zermatt-Cervinia = 20 000 hectares
Portes du Soleil = 37 000 hectares

Thanks everyone you have given me a great place to start, I had no idea where to even begin!! I'm sure I will have more questions as the winter gets closer.

"3 vallee with courchevel/meribel/val thorens is one of the biggest resort in the world."
and yes, geneve is in switzerland! near to france...
sorry!

in terms of hectar you are right that Portes du soleil is the biggest.

But probably 3 valles is the biggest in terms of all lifts and slopes linked togehter, which is in Portes du soleil not the case.

its 600 km of slopes and 200 lifts cramped onto 'only' 10 000 hectares.
U do the math.

There are plenty of well linked skiing areas larger than 3 Vallées just less exploited/crowded like for example Tignes-Val d'Isere, the Chatel-Avoriaz-Les Crosets triangle in Portes du Soleil, Ischgl, Zermatt, etc... etc..

+ 3 Vallees has bad crowds, bad snow, bad parks...
it's crappy. don't give people bad advice.