It depends from what you are looking for.
If you wish to see the city and just travel around then summer. From June till September there are plenty street performances and various free of charge events going on in Strasbourg. City is brimming with action. Also it is warm so perfect weather for outdoor picnics and visiting other gorgeous little towns in the area. Strolling in the Alsacien vineyards, castles, mountains, vine tasting etc.
September - October is for grapes picking. This is also an attraction that everyone who wish can participate :)
Spring is for MAGNOLIAS. City has a big park with few massive Magnolia trees there. In spring, when they start to bloom the view is absolutely breath taking.
But all in all I'd say summer for a good weather since there are so many things to see and do (not only in town but around as well... "Vine route" wink wink) :)
Thanks for your detailed reply. Based on your explanation, spring and summer might be my choice to visit Strasbourg :)
Good choice :) I hope you will enjoy much!