You typed 4x4 is this 4 inches by 4 inches or 4 feet by 4 feet?
If it's inches you can get printable adhesive paper from most any office supply place and you'll need a way to apply a clear laminate over the top if you plan to put the decals outside.
If it's feet you want, you are better off paying a graphics place, the parts add up. Computer (fast, lots of memory) graphics program, rip program to send file to the printer, large format printer with outdoor ink, printable vinyl and a laminator to apply the clear vinyl laminate to protect what you print. The ink, vinyl and laminate all have to be compatible with each other and your rip software will have to have the right profile to match your ink and vinyl.