study English here long

Either form is acceptable. The first sentence would probably be spoken more commonly, at least by speakers of the American language.

One problem you have is that the second sentence:--"I don't intend to study English here for a long time"--could easily be construed as meaning that you intend to study English here, but not until a long time has elapsed. The meaning of the second sentence is sufficiently ambiguous that i would prefer the first.

An improvement over both would be: "I don't intend to study English here for very long."

Many thanks.