The most popular big cages for syrians are the zoozone 2, hamster heaven, mickey 2xl, savic ruffy 2, ferplast criceti 15 and of course, a homemade bin cage. These all provide a lot of space for running around and putting in toys. You can see the different pros and cons in the cage review section, and the housing section should have quite a lot of info and pics about each from people deciding/celebrating their new cage.
Basically the recommended minimum base size for a syrian is 80x50cm.