C:\Users\USERNAMEHERE\AppData\Roaming\.minecraft
On Linux it's ~/.minecraft (press Ctrl-H to show hidden folders. On Linux, all folders that start with a period are hidden)
Also, ~ means your home folder.
There's no save files in my ~/.minecraft folder.
Though it does exist.
There is a bin folder, and in that, four .jar files and a "version" along with a "natives" folder with 6 .so files.
EDIT: I'm running the .exe version on wine, btw, if that helps.
Oh, and when I try to install actual java, this happens:
syj@syj-GA-MA770T-UD3P:~/usr/java$ sudo ./jre-6u23-linux-i586-rpm.bin
Unpacking...
Checksumming...
Extracting...
UnZipSFX 5.50 of 17 February 2002, by Info-ZIP (Zip-Bugs@lists.wku.edu).
replace jre-6u23-linux-i586.rpm? [y]es, [n]o, [A]ll, [N]one, [r]ename: a
error: invalid response [a]
replace jre-6u23-linux-i586.rpm? [y]es, [n]o, [A]ll, [N]one, [r]ename: A
inflating: jre-6u23-linux-i586.rpm
./jre-6u23-linux-i586-rpm.bin: 160: rpm: not found
Done.
syj@syj-GA-MA770T-UD3P:~/usr/java$
What's rpm: not found, mean?