Austria! It's the best place to go for an Alpine holiday if you don't want to break the bank.
We stayed at the Sportkamp Wolfgut in Zell am See, with Keycamps but there are plenty of chalet style hotels, around that area if you don't like caravan holidays. Our Keycamp guide gave us the best advice, and told us to get a Kaprun card. here You have to book a qualifying hotel, but the card includes a ton of amazing stuff to see and do! We paid for our cards, as we were staying with Keycamps. I'm not sure if that is still an option, but the camp we stayed at had a qualifying hotel on site.
We went down, river gorges, around castles, a boat tour, to two gorgeous spas, all sorts included with the card! It was an amazing week, which we hadn't really planned for until we found out about he Kaprun card.
As well as all the activities to see with the Kaprun card, you can drive up the Grossglockner, and see the biggest glacier in the alps, and see the marmots. We also went to Salzburg, saw Monet's house. There is also the tallest waterfall in Europe - the Krimml Waterfalls.
The food is fine, lots of pizza places, or German style cuisine.
Switzerland is very very expensive. When we went to Switzerland, we stayed just over the border in a French area of Geneva city, and tended to eat in France rather than in Switzerland!
The Italian alps are lovely, and eating out in some areas is cheaper. Tho not sure how much there would be to do there compared to Austria. If you are looking at Como area, it would be pricy.