The best way to see if an exchange is eligible to do business in your state is to go to your state's Office of Financial Regulation website and do a search for a license or charter.
Unfortunately, Kraken, Poloniex, and Bittrex use a "Restricted Location" clause in their terms of service agreement. If you ever see this, it means that they are not licensed in the majority of states in the U.S. and some countries. They are operating as under-compliant companies and they will just try to blame you for not knowing the laws in your state. It also means that they are not financially strong and they could have a number of security risks. These are all red flags because they cannot meet the high regulatory requirements for operation. Note Kraken has been sued recently.
https://news.bitcoin.com/class-action-lawsuit-exchange-kraken/So far Coinbase and Gemini have met and exceeded most of the regulatory requirements in the United States of America as of Oct 2017. Their website has a list of approved states. Not all states are approved because some states like Hawaii have taken a strong stance against crypto (politics). Coinbase is pretty much the de-facto standard and Gemini will probably be the future of a Wall Street style crypto exchange. Bitflyer USA is currently getting licenses in most states and should open close to next year (2018).
Approved States for Coinbase
https://www.coinbase.com/legal/licensesApproved Countries for Coinbase
https://www.coinbase.com/global?locale=en-USAreas of Operation Gemini
https://gemini.com/areas-of-operation/If an exchange is not clear about their legal stuff, then it is best not to do business with them. Never use peer to peer exchanges like LocalBitcoins. You may indirectly violate a number of financial laws by acting as an unlicensed broker or money transmitter. They're also plagued with fraudsters because of the poor escrow and verification systems. They are like the Craigslist of the Bitcoin world. Several people in Michigan and Florida have been arrested for trying to exchange crypto by themselves. Always use an approved and regulated exchange because you could be accused of indirectly supporting criminal activity or violating laws without realizing it.
https://www.coindesk.com/michigan-man-charged-unlawful-bitcoin-exchange/You should never exchange with strangers. Whenever you exchange stuff, it should pass through a proper exchange because they have to filter out all of the bad players. The downside is higher fees due to regulation. Unfortunately, not all of the exchanges out there have been inspected thoroughly. Eventually, regulators will pressure the weak ones. You can see BTC-e was seized by the government and Bitfinex bowed out because U.S. regulation was too complicated.