Learn French: La capitale est une très grande ville.

You are right that most French adjectives go after the noun. However, adjectives describing size (like grand and petit) are common exceptions that come before the noun. A helpful trick to remember these exceptions is the BANGS rule: Beauty, Age, Number, Goodness, and Size.

Because of the word très, could I move the phrase after the noun and say une ville très grande?

While not strictly grammatically incorrect, it sounds unnatural in this context. Because grande is a size adjective, it strongly prefers to stay in front of the noun. Adverbs like très (very) just tag along for the ride, so the entire phrase très grande stays before ville.

Is there a difference between la capitale and le capital?

Yes, a big one! La capitale (feminine) refers specifically to a capital city, like Paris or London. If you use the masculine form, le capital, it changes the meaning to financial capital, like money, assets, or investments.