Where do I put bootloader in Ubuntu?

The GRUB 2 files will normally be located in the /boot/grub and /etc/grub. d folders and the /etc/default/grub file in the partition containing the Ubuntu installation.

Where is GRUB installed?

GRUB (some of it) is installed in the MBR. The MBR are the first 512 bytes on a disk. The MBR is also used by the partition table of the disk, therefore GRUB itself has somewhat less space than the 512 bytes.