Here's an ideal itinerary for 6 days in Almaty:

Day 1: Arrival and City Tour

• Arrive in Almaty and check into your hotel
• Start your day with a city tour to get a feel for the city and its history. Visit the Central State Museum of Kazakhstan, which showcases the country's history and culture.
• Head to the Panfilov Park, which is home to the Zenkov Cathedral, a beautiful wooden church that is over 100 years old.
• End your day with a visit to Kok-Tobe Hill, where you can enjoy panoramic views of the city and take a ride on the cable car.

Day 2: Medeu and Shymbulak

• Start your day with a visit to Medeu, a high-altitude ice skating rink that is one of the highest in the world.
• Take a cable car up to Shymbulak, a ski resort that offers stunning views of the surrounding mountains.
• Enjoy lunch at one of the resort's restaurants before heading back down to the city.

Day 3: Big Almaty Lake and Almaty Zoo

• Take a day trip to Big Almaty Lake, a beautiful turquoise lake surrounded by mountains.
• On your way back to the city, stop by the Almaty Zoo, which is home to a variety of animals including tigers, lions, and bears.

Day 4: Charyn Canyon

• Take a day trip to Charyn Canyon, a stunning natural wonder that is often compared to the Grand Canyon.
• Enjoy a picnic lunch in the canyon before heading back to the city.

Day 5: Green Bazaar and Almaty Arbat

• Start your day with a visit to the Green Bazaar, a bustling market where you can find everything from fresh produce to souvenirs.
• After lunch, head to Almaty Arbat, a pedestrian street lined with shops, cafes, and restaurants.
• End your day with a visit to the Almaty Opera House, which is known for its stunning architecture and world-class performances.

Day 6: Departure

• Depending on your flight time, you may have some free time to explore the city before departing.
• If you have time, consider visiting the Ascension Cathedral, a beautiful Russian Orthodox church that is over 100 years old.
• Depart Almaty with memories of a wonderful trip!