Denmark is probably the best choice, an extremely developed and smart country, transparent and encourage Bitcoin business (encourage all technologies).You also have scandinavians countries : Finland (localbitcoins is there), Sweden, Norway.Other countries where exchangers are Registred are : Hong Kong, Japan, Taiwan.The only countries to avoid are :The United States.Weak European countries (France, Estonia and so on).Undeveloped countries.

There are always those safe havens in the Caribbean area, i.e. British Virgin Islands, that are lenient for cryptocurrencies. Granted they are also those same places that shady businesses go to so that their information remains private before they scam the uninformed out of their coin/cash. What is your plan for an exchange btw? Do you have a current white paper for potential investors/users to read to get familiar with your project while you're setting up your residency? I think putting something out there for people to read and potentially comment on could improve your project and get people there when you come online. Just my 2 sats.

You might consider establishing the same business in a third-world country which allowed the operation of a cryptocurrency exchange. Doing business in Asia can be a good choice...so maybe take a look at Thailand or the Philippines where cryptocurrency business is now legal and the government is more inclined and lenient to fintech companies. Of course, there are so many choices you may consider seriously as costs and legal requirements can vary from country to country.

the answer is perhaps dependent on whether or not you want to operate legally within the US. The total cost to obtain the requisite licenses in the 48 states and Dist of Columbia that require a license is approx $100,000 in application and bonding fees. The time for each state varies, but having done it i will tell you it is a fairly involved task

If you are keen to operate offshore, follow where the licensure is easy to obtain. Belize has a rather simple and quick process for obtaining a money transmitter license and the application fees are minimal . The corporate formation costs are also minimal. The Cook Islands is also a great jurisdiction with major banks being located there, the price is a bit more however.

I have a few thoughts on this if you care to chat - feel free to PM me

You probably don't realize what is the currency exchange. This is not only a huge amount of working capital but also the conditions of strict control over the transactions. Constant struggle with hacker attacks. All this in a great risk to fail. Why are you doing this? It seems to me that you need to match their capabilities.

Why are you doing this?