I need an offline installer with most of the utilities commonly needed. Somehow the default installer confuses me with all its package selection. I installed Cygwin but I can't find the diff utility after the installation.
If all you want is the UNIX command line tools I'd suggest not installing Cygwin. Cygwin wants to turn your Windows PC into a UNIX Workstation which is why it likes to install all its packages.
Have a look at GnuWin32 instead. It's Windows ports of the command line tools and nothing else. Here is the installer for the GnuWin32 diff.exe. There are offline installers for all the common tools.
(You asked for offline installers but in case you ever want one later there is a tool which will download and install everything for you.)
Method 2: make an offline install zip file for cygwin.
Don't mess with saving packages because the installed directory for cygwin can be canned in a zip file and expanded whenever you need it on any computer.
Download Cygwin installer
pick packages you want installed from gui.
hit install and wait a really long time for everything to download.
zip up the C:\Cygwin folder. Now you have your offline zip file for installing cygwin on any machine.
Unzip this file on whatever computer you like. set cmd.exe paths appropriately to point to cygwin bin directory under windows control panel.