"the only left independent bookstore"
Is:
I will go to the only left independent bookstore in my city
a correct expression?
It doesn't sound exceptionally good to me... could you advise on how to express the same meaning in a better way?
Solution 1:
There are some adjectives that do not precede the noun they modify, but the follow it.
Left, in the sense of remaining (and coming from the verb leave) is one of those.
Note that strictly speaking left as opposing right is an adjective, but left meaning "remaining" is a participle that can be used attributively. It is used in some ways like an adjective, but it's not exactly the same thing.
We can use left preceding a noun, but then it is the opposite of right:
Will you take the left door or the right door?
If I remove one of the two doors:
There is only one door left.
So the correct phrasing of your sentence would be
I will go to the only independent book store left in my city.
Unless you do mean a book store that sells books expressing specific political views...
Solution 2:
In idiomatic American English, we would tend to say, "I am going to the only independent bookstore left in my city".
A "left independent bookstore" implies they are politically-leaning to the Liberal end of the spectrum. And that might be what is meant - but it's most likely not.
Solution 3:
"I will go to the only independent bookstore left in my city" or, preferably, "I will go to the only remaining independent bookstore in my city"
Solution 4:
The normal construction would be 'the only independent bookstore left in my city', with the presumption that all the other bookstores in town were chain stores.
In some cities where political specialty bookstores can thrive (San Francisco or London, e.g.), then it is possible the speaker could mean the only left-wing or leftist bookstore, but then "independent" would probably be redundant.