I’m from the EU and my budget is about 3500 euro including flight(s).
Some countries that are on my mind: Colombia, Thailand, Indonesia, Ghana, South Korea, Japan.
Vietnam in October is fairly nice in the north. Starting to cool down at night a bit. Spend a week to ten days in Vietnam going from north to south (Hanoi, Halong Bay (and possibly Ninh Binh), Danang/Hoi An, and Saigon) and then then 3 days in Siem Reap, Cambodia to visit the Ankor Temple complex and then a few days in Thailand (Bangkok and the nearby Ayuthaya temple areas and maybe fly down to Phuket or take a bus to Pattaya).
@fitobugger2017 @tebessa fully recommended Ayutthaya, impressive place, I can’t even fathom that place during the cusp of the Siam civilization, as ruins they are impressive!!!
It will be autumn in South Korea and Japan and will get cool as you get later into October. Airfare alone will probably be about 1/3 of your budget.
How do you like to travel? Do you stay in one city and do day trips to outlying areas? Are you planning to backpack your way through the country, staying 2-3 days in each location?
Are you adventurous with food?
What type of accommodations are you looking for? Hostels? Airbnb?