Lots of people go to ski resorts and don't ski, though you might find cross country ski-ing to your liking. It's really just walking with skis on, it's on the flat and you can make it as easy/difficult as you want. I no longer ski but often have a holiday in the mountains in winter. When I worked as a ski instructor though I taught ladies older than you Shirley.
Doe recommended Lech, it's one of my favourite resorts, I've been there loads of times in fact it's where I learned to Ski some 40 years ago. It is a pretty pricey resort though, as is much of Austria these days. Lech is where Princess Diana often used to ski with the boys.
Non-skiers can ride the chair lifts and cable cars up to the top of the mountains (or halfway stations)and sit in the sun or in the cafés and watch the skiers/snowboarders flying past. Lots of resorts will have extra activities such as horse drawn sleigh rides on offer.. Many hotels will have some sort of entertainment at night.
If you aren't going to ski you will probably be best in a reasonable sized resort, many resorts have swimming pools, shops and walking trails. If you are lucky with the weather you could come back with a great suntan. If you do choose Austria, Seefeld, Kitzbühl, Zell am See, Ischgl, Sölden and Obergurgl come to mind. Though not one of my favourite ski-resorts St.Anton has been a popular destination with British winter sports fans for a long time now.
Sorry I can't be of any help with Bulgaria as I have never been there I believe though it's a cheaper option than Austria but I don't know what there is there for non-skiers.