Here's a list of rooms in Günzburg: pension-guide.de Guenzburg
There are some really cheap ones, just take a look at "Privatzimmer Lacher" for example (single room starting at 10 Euro/night). However, note that these are mostly small boarding houses run by the owner, which means not everyone will understand English.
I think it's a good idea to check the walking/driving distance from Legoland for each address first - maps.google.com might be helpful here. Good luck!