"Mis padres quieren visitar diferentes pueblos."
Translation:My parents want to visit different towns.
From what I can tell, "mis padres quieren visitar pueblos differentes" would be closer to "... to visit towns which are different/unique" and "mis padres quieren visitar differentes pueblos" is closer to a disagreement over which town to visit "each of my parents wants to visit a different town"
There must be some rule to when the adj. follows the noun and when it is in front. That would be nice to know.
I saw this explanation which might help https://www.spanishdict.com/guide/adjective-placement
Before noun it means something like 'various' - my parents want to visit a variety of towns. After noun it may carry the meaning that there is a disagreement.
Why do we not say visitar a differentes pueblos here? Is the a not necessary for the unconjugated form visitar?
You only need the a when you're visiting people---it's that Spanish personal a, not used when visiting places.
Very close! A mi padre le gusta Guadalajara, y a mi madre, Oaxaca.
Se gusta means is pleasing: Se gusta la primavera aquí.
can only adjectives ending in "e/es" go before the noun or can all adjectives go before the noun?
Nope, many "ordinary" adjectives can precede the noun. Examples: blanca nieve and nieve amarilla. An adjective before a noun often takes on an intrinsic, almost poetic quality: "The white snow glistened in the morning sun". Whereas after a noun, it suggests a more restrictive, specific instance: "Children should be told not to eat yellow snow." Another classic example: Nueva York.