You might have a rogue app draining the battery. Mine lasts all day with close to 50% by the time I get home. One day I t tried my hardest to kill it and after a 20 hour day I still had 15% left with 7 hours of screen time. I really hope you find out what it is. ..
You could check in Menu>Settings>Battery to see what is using most of your battery.
For a much more detailed view of what's happening, install GSam Battery Monitor from Play store. There is a free version. It will show exactly what apps or processes are sucking the life out of your battery.
One app that I know kills the battery is Words With Friends. I get up every morning and unplug my phone from the charger at 6:30. With my normal usage, by the time I go to bed around midnight or 1 am, the battery level will be at around 30 percent. However, if I am going back and forth with my wife on Words With Friends for that day, the battery will hit 30 percent around 7 or 8 pm.
My Note 2 goes all day also. I start at 100% in the morning and at 40-50% at night when it goes on the charger and that is with EVERYTHING synced. 4 Email accounts, Facebook, Twitter, Engadget and BW.
It shouldn't take very long at all to fully charge your battery if you are using a 2A Battery Charger (The one that it came with) Also want to make sure you have a proper cable that allows for that much power to go through. Not all USB Data/Sync cords charge at the fast pace with the 2A charger.