Avoid the school holidays when the whole country floods to the slopes. Georgia and Russia share the Caucasus mountains, the highest in Europe. Skiing can be fabulous, though the lift systems are under-developed and medical facilities, hotels, transport and communications can be dreadful. Italy is relaxed and stylish, with good skiing and food. Resorts near to big cities are prone to overcrowding.
Japan offers good, though expensive skiing.
Areas are frequently extremely crowded, signs are in Japanese and there may be few rental boots for Western bigfoots. New Zealand is better for heli-skiing and cross country than for alpine skiing. The season lasts from July to September. Scandinavia has numerous small resorts that offer alpine skiing. It is expensive, but great for cross-country skiing and saunas.