Whilst the official currency in the TRNC is the Turkish Lira, they will also accept the Euro 9though you will get a "rounded-up" exchange rate and I believe sterling and other currencies will also be taken in some cases.
Whether you get a better exchange rate depends on where you change your money, but here in the South many visitors find it easier to just bring a few euros for the first day, then either use their cashpoint card to withdraw money or go to one of the many foreign exchange offices or the bank.
Remember that many parts of the TRNC are remote so you will only be able to change money in major towns like Girne (Kyrenia). So unless you take enough cash with you, in any currency, you may not be able to get additional money unless staying near Kyrenia.
Nicosia, of course, is part TRNC, so you can easily get cash there if you need it.
