Consider the following Dell Inspiron 5000 for $399 + shipping which comes with the AMD A10-7300 APU and has the integrated Radeon R6 (Kaveri) GPU. It is more powerful than the Intel HD 4600, but less powerful than the nVidia GT 720m.
The following is a review for the Acer Aspire E5-551-T8X3 with the same APU. However, it is in German, but you can use Google to translate it. There are some gaming benchmarks near the end of the review.
Here is another option with AMD previous generation APU; 15.6" ThinkPad Edge E545 20B2000YUS. It uses the slightly older A10-5750m APU with the integrated Radeon HD 8650g graphics core. It is a bit more powerful than the nVidia GT 720m. It costs $400 + shipping.
Since this is a ThinkPad it is a business laptop. That means this does not have a glossy screen which reflects light like a mirror. It has a matte finish screen which does not reflect light directly back at you. This means it can be used in bright settings including outdoors. However, matte finish screen do not make colors look as vibrant as compared to glossy screens.