In Ban Phe there is not much shopping, it is a small village with small shops and some groceries.
Inside Rayong there are major department stores and shopping centers, the most popular are Laemthong and Central Plaza.
If you are really serious about shopping, we recommend to go to Pattaya or perhaps spend your last days in Bangkok.
Take a look at our map over Ban Phe and Rayong to see what kind of shopping that you can do. A recommendation is the Friday night market near Tesco Lotus in Rayong, here you can find a lot of stuff!