Postcard
Getting a Pen Pal is easy; Go to the Socialize menu on the computer, Click: "Find a Pen Pal", Then wait a few hours. You may get a Pen Pal. Click on the Same "Socialize" Tab, Write to them for a while, Then you will get the option "Ask For Postcard. There is a chance you will get a postcard next day in the mail.
All Postcards
These are all the Postcards and their Rarity:
Sunset Valley Common 20$
Appaloosa Plains Common 20$
Riverview Common 20$
Littlehaven Common 20$
Bridgeport Common 20$
Lucky Palms Common 20$
Moonlight Falls Common 20$
Twinbrook Common 20$
Lunar Lakes Uncommon 50$
Champ Les Sims Uncommon 60$
Barnacle Bay Uncommon 55$
Midnight Hollow Uncommon 50$
Isla Paradiso Rare 120$
Dragon Valley Rare 135$
Notes
-It is not 100% sure you will get a postcard next day in the mail.
-You Can get a Pen Pal Multiple Times
-You cannot get a Pen Pal Using your Phone
-If you don't get the "Ask For Postcard" interaction right away, try writing to your Pen Pal some more.