This seems to be related to
the symbols on the number keys of a computer keyboard, read left to right. I initially thought each line referred to one key, but now I think each symbolizes a block of consecutive keys.
Oh! I am so excited!! This is my first puzzle!
Exclamation mark '!'
I can show you where the things are. Ready for a quick game?
At-sign '@' (on US keyboards) followed by '#' perhaps symbolic of tic-tac-toe (thanks to user IdiotStyle for this suggestion). Or maybe '@' is for the game Nethack, but that's not quick unless the player is unlucky or careless.
I am rich you know! I can be usually in a command, or a hat.
Dollar sign $ symbolizing money, followed by '%' used for variable substitution in MS-DOS/Windows commands, followed by '^' (informally called a hat). Or maybe they're all $ (rich: obvious; command: Unix shell command prompts; hats full of money are a bit of a cliche).
I am famous, I am in maths , I am the sun.
Star (asterisk) '*'
Open me... close me, you will get less or more
Parentheses '(' and ')' followed by '-' and '+' (we're now no longer on the number keys, but still on the same row of the keyboard).