Turkey is remarkably open with allowing guests access to its Mosques; they are closed to visitors only during times of prayer. Guests do have to comply with some basic guidelines (i.e. women need to cover their hair/shoulders, and they should not be showing too much leg; all visitors also need to remove their shoes). At most mosques, however, scarfs are provided for free use, and there are locations where shoes can be left outside (or plastic bags are available to carry inside.) At some mosques there are even Imams available that you may ask questions about Islam to clarify any perceptions one may have about Muslims and the Islamic religion.