The closest major airport to Almaty International Airport is Manas International Airport (FRU / UAFM). This airport is in Bishkek, Kyrgyzstan and is 274 km from ALA. If you're looking for international or domestic flights to FRU, check the airlines that fly to FRU.
Travelmath helps you find the closest airport to any city, as well as a list of smaller local airports. You can use these pages to plan your trip and figure out the easiest way to get to your destination. Many times there are multiple airports near the city you want to visit, so you can often find a cheaper flight into a different airport. This is especially useful if you are getting a rental car, since it might be better to drive a bit farther in order to save money on airfare. If you're booking an international flight, you probably want the closest major airport, otherwise if you're a pilot you may be looking for a local airport. Use this tool along with the flight distance pages to plan your travel.