My older brother wants to take me to another country, but we already have been to France, Britain, United States, Mexico, Australia, Greece, and Japan. Please, I want the recommendation not too bizarre but something that's not in one of the countries previously listed. :-)

Thailand or Vietnam.

This is a great question. There are plenty who would recommend India - such a standard and well-regarded travel destination, but it might be in the "bizarre" category. If you want something more mainstream but still exotic, I would recommend Turkey (since you've been to Greece you might see similarities). Alternatively, Spain is great place to go - look into Barcelona and the Catalan area. Finally, a cool and interesting country that is very European but also very Eastern European is Slovenia (Ljubljana/Lake Bled).

Follow-up here with what you end up deciding.

I guess not Egypt right now, But you were in the US, but what part, Alaska has some real adventure spots. Canada has wonderful fishing and hunting ( if you like that sort of thing)

Israel has wonderful history

Dubai, Virginia, Mauritius and Maldives are some good choices for vacations. Also consider them.