Where does metadata go when you save a file?

It's not stored in that file. It's stored in the filesystem, and all parameters are copied manually one-by-one (though some cannot be copied at all).

That is, most operating systems don't really have a "copy file with metadata" call. The file-copy program just creates a new file named foobar.py, copies the whole 0 bytes of data, then uses utime() or SetFileTime() to make its modification time look the same as the original's. Likewise, file permissions would be "copied" by setting them anew using chmod() or by copying the POSIX ACL attribute.

Some metadata isn't copied. Setting ownership requires root privileges, so copies of someone else's files belong to you and occupy your disk quota. The ctime (attribute change time) is impossible to set manually on Unixes; btime (birth/creation time) is usually not copied either.

Compare cp -a foo bar (which copies metadata) and cp foo bar (which doesn't):

$ strace -v cp foo bar
…
open("foo", O_RDONLY)                   = 3
open("bar", O_WRONLY|O_TRUNC)           = 4
read(3, "test\n", 131072)               = 5
write(4, "test\n", 5)                   = 5
read(3, "", 131072)                     = 0
close(4)                                = 0
close(3)                                = 0
…

$ strace -v cp -a foo bar
…
 -- original metadata is retrieved
lstat("foo", {st_dev=makedev(254, 0), st_ino=60569468, st_mode=S_IFREG|0644,
             st_nlink=1, st_uid=1000, st_gid=1000, st_blksize=4096, st_blocks=8,
             st_size=5, st_atime=2016-12-28T09:16:59+0200.879714332,
             st_mtime=2016-12-28T09:16:55+0200.816363098,
             st_ctime=2016-12-28T09:16:55+0200.816363098}) = 0
 -- data is copied
open("foo", O_RDONLY|O_NOFOLLOW)        = 3
open("bar", O_WRONLY|O_TRUNC)           = 4
read(3, "test\n", 131072)               = 5
write(4, "test\n", 5)                   = 5
read(3, "", 131072)                     = 0
 -- modifiction time is copied
utimensat(4, NULL, [{tv_sec=1482909419, tv_nsec=879714332},
                    {tv_sec=1482909415, tv_nsec=816363098}], 0) = 0
 -- ownership is copied (only with 'sudo [strace] cp')
fchown(4, 1000, 1000)                   = 0
 -- extended attributes are copied (xdg.origin.url is set by browsers, wget)
flistxattr(3, NULL, 0)                  = 0
flistxattr(3, "user.xdg.origin.url\0", 20) = 20
fgetxattr(3, "user.xdg.origin.url", "https://superuser.com/", 22) = 22
fsetxattr(4, "user.xdg.origin.url", "https://superuser.com/", 22, 0) = 0
 -- POSIX ACLs are not present, so a basic ACL is built from st_mode
 -- (in this case, a simple fchmod() would work as well)
fgetxattr(3, "system.posix_acl_access", 0x7ffc87a50be0, 132) = -1 ENODATA (No data available)
fsetxattr(4, "system.posix_acl_access", "\2\0\0\0\1\0\6\0\377\377\377\377\4\0\4\0\377\377\377\377 \0\4\0\377\377\377\377", 28, 0) = 0
close(4)                                = 0
close(3)                                = 0
…

It generally differs from filesystem to filesystem where the metadata is stored. On the ext2-family of filesystems, the metadata you mentioned (owner, group, permissions, time) are stored in the inode. The inode also stores (pointers to) the blocks the file occupies on disk. The inode does not store the filename.

You can access this data with the stat system call (man 2 stat), and use the stat tool to print it (man stat). A detailed description of the inode fields can be found in linux/include/linux/fs.h in the kernel source.

There are other kinds of metadata (e.g. ACL permissions) that are stored in different places.

Metadata is not copied by default when you copy the file. Instead, a new file with default metadata values is created. There are various options to cp (-p, --preserve) which instruct cp to also copy metadata, by reading the old metadata with stat and modifying the new metadata accordingly.

Depending on the file system, areas are reserved either (semi-)statically or dynamically to hold metadata such as permissions, size, and others (sometimes the file name too).

In Unix, metadata is stored in the inode controlling the data area where the file resides (while file names and related inode numbers are stored in a directory entry).

In some filesystems directory entries are files like any other, but hidden from view. FAT and FAT32 are such filesystems (FAT's root directory is "special" though). When you create a file, you add/edit an entry in the file that describes the folder where the file resides. Each entry is large enough to store file size, name and date, and nothing else (long names occupying multiple entries; the default entry size of 32 bytes can hold a single name in the old 8+3 character format. All this, of course, assuming my memory is working). Ext system is similar, but the directory entry is dynamically sized and holds only the name and the inode pointer; all other information is in the inode. This way, two entries may point to the same file, which is useful to manage duplicate files.

In some filesystems, inodes can be large enough to hold a small amount of data in addition to the metadata, so that if the file can fit there, it does not occupy extra disk space. You create a 45-byte file and the free disk space does not change at all; those bytes are stored inside the inode. I think that the ext* family supports this (and NTFS too). This helps to manage large number of very small files.

In yet other file systems, there's what amounts to a "phantom" file system along the main one, that stores these extra attributes. Not only file information but possibly file icons as well.

Some systems have both: NTFS has the full directory metadata working in inode-like fashion, and the possibility to create alternate data streams holding further information that does not (apparently) change anything in the "main" file.