This can either be done with a JOIN or a UNION clause. Depending on what you want your result to look like. (I'm making some assumptions about your schema in the following examples):
With a JOIN
SELECT *
FROM cities
JOIN countries ON (cities.country_id = countries.country_id)
WHERE cities.name = 'New York'
OR countries.name = 'New York'
With a UNION (use ALL if you can, for performance reasons)
SELECT cities.name, 'Is a city' AS type
FROM cities
WHERE cities.name = 'New York'
UNION ALL
SELECT countries.name, 'Is a country' AS type
FROM countries
WHERE countries.name = 'New York'
Using NATURAL FULL JOIN
NATURAL FULL JOIN may be used to behave similar to a UNION if you use it "correctly", as shown in this blog post or in this one.
SELECT *
FROM
(SELECT 'cities' AS source, cities.* FROM cities) cities
NATURAL FULL JOIN
(SELECT 'countries' AS source, countries.* FROM countries) countries
WHERE name = 'New York'