I don't know if this is the case in Portuguese, but in Spanish ("algo" and "alguna cosa") it wouldn't really sound quite right. It's as if you are being too specific but also staying unncessarily vague; if someone tells me they have "alguna cosa que hacer", I'm going to be left wondering why they didn't just tell me exactly what they were doing.
I guess if you REALLY wanted to say the second option, you could, but it's not the preference of a native speaker. I know that's not exactly the answer you were hoping for, but I hope it was at least a little insightful.
I'm a native speaker of portuguese and you need to know: don't worry about that, because "algo" and "alguma coisa" almost always mean the same thing. And in this case, they mean the same thing. But, it sounds more natural to say "algo".
I hope I won't confuse anyone even more, but I just wanna add that in real life we actually say "tenho uma coisa" a lot more than "algo" or "alguma coisa". And yeah, meaning we don't really wanna tell you what it is.
Does "a fazer" really make sense? I thought only "para fazer" would be acceptable.
Which means "I have to do something" and not "I have something to do", I think.
Precisely, Duomail (although the two sentences are often used with the same meaning, at least in Brazil).
Does "Eu tenho algo que fazer"? Like in Spanish "Yo tengo algo que hacer".