In these examples, "We Americans" would be the grammatically correct choice because it's the subject. Remove "Americans" from the examples and the choice is clear:
We like basketball.
Us like basketball.
But if it were the object, "us" would be the correct choice:
Basketball is important to us Americans.
These are the options if you want to be strictly grammatically correct, but you might prefer a different construction. Many regions, cultures and contexts consistently use constructions that differ from the official grammatical rules, including using "us" with an appositive even in a subject ("Us Americans like basketball"). Language is not a matter of universal moral absolutes, though, so using an "incorrect" construction is not "wrong," especially if it's what's expected and accepted in the context you're in. What's most important is for your intended meaning to be understood. So one might "prefer" "Us Americans [verb]" simply because it's commonly used in their context.
Note, the opposite idiomatic practice doesn't really happen: No one (that I know of) says "Basketball is important to we Americans."