They pretty much mean the same thing. For the former sentence, する　has been conjugated in some way to form し　( maybe as an objective verb , or maybe because there are two verbs involved ). There may be a preference depending on the person. I feel something missing , so I would say 市役所へ外国人とうろくのため行きます。

Actually, both sounds are wrong to me. I guess "市役所に外国人とうろつきにいきます" is grammatically right. But sounds so weird. You can say "街にうろつきに行く", but you can't say "うろつく" in case of "市役所". They are the example sentences differences between "しに行く" and "行く" 街へ買い物をしに行く Two verbs 街へ買い物に行く A verb

The former smells a bit slangy; the latter reads grown-up.

Cindy, oops,excuse me! i wrote the answer in your column by my carelessness. i should have wrote it in the following entry column... i am happy to hear that you understand. thanks.

Thank you very much for all your answers and different views ! I think I understand the difference now.