i3-2100 would be a better option.
I forgot to mention it's not a pure gaming computer. I know the i3-2120 (i think that's the new one) is the best option for a budget gaming build but she will be using this computer mostly for school. She told me she does want to be able to play games but it's not the primary reason for getting a new computer haha. She is an art student in college and so it will mostly be used for art stuff like Photoshop and other programs. From what i read the i3 is great for games but when it comes to multitasking and other applications, a multi-core setup is better.