I have an account still in Pattaya and moved to Buriram, and I withdraw money from the ATM via the Bank App on my Phone (cardless withdrawal) and I didn't have to pay any fees for that.
If you use an ATM card then you pay (I believe) 15 THB per withdrawal.
You cannot move the account to your new province, what you do is open a new account in the new province and then have them transfer the money to the new account.
But this will cost you (AFAIK) 150 THB per 100.000 THB transferred.
Now I leave my Pattaya account dormant but still have approx 10K in there so it doesn't get closed.
Withdrawal via the Cashier in another province then where your account is located will also incur fees. How much I am not sure.
Another solution for you is open the account in the new province and then via Internet Banking transfer money from the OLD account to the New account