When is "andare a" not used?
As I understand it, in Italian you don't say "Vado a" with a verb in its infinitive form for everything like you might do in a language such as Portuguese (Vou) or Spanish (Voy a) to say, "I'm going to...".

When is it okay to use this and when won't you want to use this and use the first person future tense conjugation of the desired verb instead? It's not very clear to me how far I can take it. Thanks!

Question

When is "andare a" not used?
As I understand it, in Italian you don't say "Vado a" with a verb in its infinitive form for everything like you might do in a language such as Portuguese (Vou) or Spanish (Voy a) to say, "I'm going to...".

When is it okay to use this and when won't you want to use this and use the first person future tense conjugation of the desired verb instead? It's not very clear to me how far I can take it. Thanks!

Answer

/vado a + verbo_infinito/  
has not the same meaning of the English 
/I'm going to + infinitive_verb/
Examples:

e1. vado a cucinare
e2. comincio a cucinare
e3. mi metto a cucinare

(e2) and (e3) both means 'I start to cook'
(e1) means two things:
- I move to another place (for instance I go to the kitchen)
AND
- /I start to cook/, OR /I continue to cook/

The expressions with the verb /andare/ at least in the vast majority of cases always imply 
the meaning of /displacement/.

Answer

In everyday language, "vado a" and "andrò" are pretty much interchangeable. Then there are people who use a form more than another, but if you choose one of the two forms you will be understood.
If you want a guideline, in my opinion you can use " vado a" in the near future (like few days or a week) and "andrò" for the further future.