You asked: I would like to take my children on a European ski trip. I’m interested in visiting a couple different countries, but I want places that are easily reachable via flights from the US, and I don’t want to spend a lot of time traveling between the two resorts. What do you suggest? – S.F., New York, NY

Based on the resorts best suited for proximity and a double culture fix, we think Kitzbühel in Austria and Zermatt in Switzerland will be the right fit. You would fly into Munich and transfer by car to Kitzbühel. Following your time there, you would take a train to Zurich, then on to Zermatt. The train leaves right from the ski resort in Kitzbühel in the early morning and arrives in Zurich late afternoon. Though it’s a long day of travel, the experience of dining aboard a European train (which is much nicer than Amtrak) can be quite memorable for children. Your return flight would be from Zurich. If you follow this itinerary, you’ll cover three countries during your time—four if you skied into Italy from Zermatt.

Kitzbühel offers world-class skiing and an Old World charm that draws an elite international crowd—think Aspen or Vail, but at half the cost. The 700-year-old town has served as an alpine paradise since 1892, but these days the 56 lifts offer modern skiers access to multiple peaks and plenty of powder. A big draw off the slopes is the Aquarena, which houses two swimming pools, a sauna and a solarium plus a massage center, casino and indoor tennis courts. While many hotels in town do not have a pool, this public facility gives kids a way to burn off energy when they’re not strapped to their skis. We recommend staying at the Hotel Maria Theresia (011-43-5356-64711, hotel-maria-theresia.at), a lovely, family-owned hotel in the center of the village within walking distance to everything. If you’d prefer that the hotel have its own pool (which is often a plus to parents), try the Schwarzer Adler (011-43-5356-6911, www.adlerkitz.at), also conveniently located and with a splendid new fitness center, spa and indoor pool.

After a week in Kitzbühel, we suggest transferring to Zermatt, a picturesque Swiss town at the foot of the Matterhorn where the only way in is by train; cars are banned from the streets. Although the idyllic village draws lots of visitors, the 155 miles of ski trails and a resort capacity of almost 40,000 people per hour guarantees against crowded slopes and long lift lines. Plus, thanks to the new Klein Matterhorn lift that ascends to 12,533 ft, you’ll have access to glacier runs that help extend the ski season well into the Spring. Be sure to take advantage of the option to ski over to Cervinia, Italy for lunch one day. Within town, the Hotel Ambassador (011-41-27-966-2611, www.ambassador-zermatt.ch) will make a great home base for a family thanks to its convenient location in the center of town and comfortable rooms.