Gōngyù de xībian shì lángiúchǎng

At the west of the apartment building there is a basketball court.
In the west of the apartment building there is a b.c.
A basketball court is at the west of the apartment building.

Looks fine to me

I think any of those translations would work. Chinese and English are obviously very different languages and you can't always reflect such subtle differences (especially in preposition usage) when translating English into Chinese.

Rodney and Rmzhao82. Thank you for your help. Greetings.

lánqiúchǎng not lángiúchǎng

Second sentence is a possible translation, but I doubt any chinese would understood the sentence as such - rare if not unheard of for an apartment building to have an internal basketball court in China - if really wanted to say this would say:

Gōngyù li3mian de xībian shì lánqiúchǎng

Seems you are using learning materials with no translation - I would suggest you use chinesepod.com or something else that has translations already at this level

For these types of questions i think italki.com to be a better solution.