If the cheapest Vaio laptop is not on your shortlist, then you should definitely check out the Sony Vaio SVE15115FXS. Featuring a 15.6 inch display, it comes with an Ivy Bridge Core i5 processor, Intel HD 4000 graphics, 6GB RAM and 750GB hard disk drive that make it good enough to handle day-to-day activities.
The HD 4000 graphics are much better than Intel HD 3000 graphics but are still no match for the middle and high end Nvidia and AMD graphics. For those folks, Sony is also offering configurations with AMD Radeon HD 7550M GPU with 2GB VRAM.
The base model comes with Core i5 3210M processor is a very capable processor and offers amazing performance for the money you are spending on it (which is 680 dollars). You find more about it in this Core i5 3210m review.