How can I set "vi" as my default editor in UNIX?

You should add it to your shell’s configuration file. For Bash, this is ~/.bashrc or ~/.bash_profile. You should also set $VISUAL, as some programs (correctly) use that instead of $EDITOR (see VISUAL vs. EDITOR). Additionally, unless you know why, you should set it to vim instead of vi.

TL;DR, add the following to your shell configuration (probably ~/.bashrc):

export VISUAL=vim
export EDITOR="$VISUAL"

On some Linux systems, you could also set your default text editor by using the following command.

sudo update-alternatives --config editor

In recent versions of Ubuntu you use the alternatives system to manage the default, editor, e.g.:

update-alternatives --set editor /usr/bin/vim.basic

To see which editors are available for use:

update-alternatives --list editor

Some UNIX distributions might provide a select-editor command:

select-editor

And it will ask you which editor to use.

Make sure you actually have vim installed before trying to set it as your default editor.