My first bit of advice is always to use some tool like Access to dummy up your tables, use the design tool to create the query you want and then view the sql.
Basically you want to:
select tours.band, city.city, country.country
from tours, city, country
where tours.cityid = city.cityid
and city.countryid = country.countryid
and country.country = 'New Zealand'
// order by country, city, band
// order by band, country, city
drop the country = 'kdsfj' if you want them all. use either of the orders depending on how you want to display your data.
HTH