Hi sonez I'd like to advise you, browse the internet, find attractive places and ask your friends or reception staff to call a taxi.
Either with a family or alone you can safely go up to the mountains: Shymbulak the highest public ski resort in Almaty (there are a lot of snow at the moment, since the last snow falling), and Kok Tobe - the hill where our city's TV broadcasting tower is. You could find a statement museum on Furmanov str (name of the street should change in the future) near the Ramstore. Â
One more interesting place is the Museum of Paint Art of Kasteev beside the National bank building and Hayatt Regency hotel.