Is places a proper noun?

No, the plural noun 'places' is not capitalized unless it is the first word in a sentence. The noun 'places' is a common noun.

The names of places are always proper noun. Proper nouns are always capitalized.

Examples:

common noun - park

proper noun - Yosemite National Park

common noun - neighborhood

proper noun - Greenwich Village (in Manhattan, New York City)

common noun - city

proper noun - San Francisco

common noun - country

proper noun - India