Most retail store do close early on New Years eve. When they close depends on the store, but its generally several hours earlier than normal. Some close at 6, some close at 7, or whatever the case may be - much like Christmas Eve.
There are other businesses that stay open, such as some 24 hour chain drugstores which never close such as the 24 hour Walgreens. Many gas stations and convenience stores also will stay open for their normal business hours and not close early. Again, it just depends on the store. But as a general rule, most businesses will close early on New Years eve.
On New Years Day, most retail stores will be open because this is the last day of the holiday season, and most will have sales going on though the best sales are already over with, such as Black Friday and Cyber Monday. However, this applies to mostly the major retail stores. You will find that most small businesses will be closed, especially the ones not directly involved with retail sales. Its a holiday, after all! But as of January 2nd, everything will be back to normal, YAY!
