Local people will sometimes be very keen to meet people from other countries, especially if they come from a country or culture that is considered to be high status. An example would be French speakers coming to Australia. Almost all Australians study the French language at some stage during high school, and read books by French authors like Jean-Paul Sartre and Albert Camus. Paris, cafes and their attitude to life all contribute to making French international students 'cool'. But what about Chinese students studying in the United States, or Japanese students going to the Czech Republic?
If you are Japanese, for example, find out if there are Japanese culture clubs or societies in the city that you are studying in. This could be things like Anime appreciation clubs, or Calligraphy groups. These people are locals, and the very fact that you are from Japan makes you an expert, valuable and interesting.
You find these things by searching in the local language, 'Japanese culture club Melbourne' other examples would be: 'Spanish Language Exchange Group Israel', 'Russian Music Club Boston', 'Cricket club Prague'. The internet is a powerful tool. Make sure though that when you look for Cricket club Prague, that you actually search for it in Czech - so 'kriket klub v Praze'. If you search for Russian groups in Russian, the chances are they will all be from Russia, and you won't meet local students.
Generally, if you always speak about learning English as your main interest, then native English speakers won’t be very interested because they already know how to speak English perfectly. If they wanted to tutor people in English they would probably want to charge money.
The ultimate though is joining language exchange groups because for example in a not-for-profit organisation, for example, all of the local Australians are interested in meeting native speakers from Japan, China, Korea or Taiwan because they are either learning to speak Japanese, Korean or Chinese, or they want to go to one of those countries. And similarly all of the Korean students want to meet locals so that they can make friends with them and improve their English – but more about language exchanges later.