Hi Natalia!
I live now since 2008 in Stuttgart. Life is good but quite expensive - not München expensive though.
I dont't work in your field, but i know that pixomondo, the ones who do the dragons in game of thrones, have a quite big office there.
Rent skyrocketed in the last years, and it is almost impossible to get your own flat in the hip neighborhoods, if you don't work for daimler or bosch and earn a shit load of money ...
But you can allways find a WG, try to avoid september/oktober when the new students arrive in town.
Stuttgart is a very conservative but also green oriented city with an air polution problem.(feinstaub)
You don't need to worry about safety ... once I forgot where I left my bike, and stmbeled opun it one year later ... it was still there, untouched, at Feuersee.
However I decided to move to Berlin. For my taste Stuttgart is to far right in the political spectrum, and financially you are a second class citizen if you don't work for daimler(mercedes) or bosch ...
I hope this was helpful and wish you good luck!
Adrian