Where to put location words in a sentence
In &quot;她去了中国很多地方&quot;, 地方 (place) is the object, 中国(的) (China's) is an adjectival phrase, along with 很多 (many), modify the object 地方


The break down:
&quot;她去了很多地方&quot; -  &quot;She went to many places&quot;
&quot;她去了(中国的)很多地方&quot; - &quot;She went to many (China's) places&quot;
the possessive  的 is omitted in your original quote
&quot;她&quot; is the subject &quot;去了&quot; is the verb;  &quot;中国的&quot; and &quot;很多 are the adjectival phrases; &quot;地方&quot; is the object

Since &quot;中国(的)&quot; and &quot;很多&quot; are both in adjectival roles, you can change their order and write &quot;她去了很多中国(的)地方&quot;

In &quot;她在中国去了很多地方&quot; , &quot;在中国&quot; is the 'relative phrase' that provides additional information to the 'main clause'


The break down:
&quot;她去了很多地方&quot; -  &quot;She went to many places&quot;
&quot;她(在中国)去了很多地方&quot; -  &quot;She went to many places (in China)&quot;
&quot;她去了很多地方&quot; is the main clause; &quot;在中国&quot; is the relative phrase

Question in your post title:

Where to put location words in a sentence?

In English, location usually precede time, e.g &quot;See me in Central Park tomorrow&quot;
In Chinese,  time usually precede location, e.g  &quot;明天在中央公園見我&quot;

I asked my dad who's fluent in Mandarin, and he says both are find, but the first sentence is more commonly used. Why is that?

Neither one is more common than the other. The two sentences have different emphasis. &quot;她去了中国很多地方&quot; emphasizes on her 'achievement' of visited many places in China; &quot;她在中国去了很多地方&quot; emphasizes on her 'actions' in China, which included visiting many places.