Kaminoge - It says you are in Bulgaria - not sure if that is correct.
If you are a non tax resident of Australia, investing in Australian blue chip shares is pretty good in that you will not pay any Australian tax on the capital gains and generally the dividends are fully franked.
Just get a portfolio of blue chips (BHP, Telstra, banks etc) or you can buy shares in a listed investment company.
If you get an online broker the fees are fairly low (only trading fee) and no investment fees.