API keyは自分のものに置き換えてください。

Encoding.default_external = 'UTF-8'
require 'json'
require 'open-uri'

# @here = params[:here]
# @dist = params[:dist]
@here = '東京'
@dist = '大阪'

url="https://maps.googleapis.com/maps/api/distancematrix/json?origins=#{@here}&destinations=#{@dist}&mode=walking&language=ja&key=YOUR_API"
puts @obj = JSON.load(open(URI.encode(url)))

@destination_addresses= @obj['destination_addresses'][0] ;
@origin_addresses= @obj['origin_addresses'][0] ;
@km= @obj['rows'][0]['elements'][0]['distance']['text'] ;

puts "現在地"
puts @here , @origin_addresses
puts "目的地"
puts @dist , @destination_addresses
puts "距離"
puts @km