Any 11 inch laptops that has Intel HD 4000/4400/4600 etc..?

Solution
The Lenovo X220 can be purchased for less than $300 at Newegg. However, it only has a Sandy Bridge generation Core i5 CPU which means it has the Intel HD 3000 graphics core.

http://www.newegg.com/Product/Product.aspx?Item=9SIA1ZD3208651&nm_mc=KNC-GoogleMKP-PC&cm_mmc=KNC-GoogleMKP-PC-_-pla-_-All+Laptops+%2f+Notebooks-_-9SIA1ZD3208651&gclid=Cj0KEQjwvo6wBRCG3Zv92ZSLlIYBEiQA5PLVAts1OVV9brq6aSBOcX4ZeidPHFQTcHAym0xkMCESRyQaAsWw8P8HAQ&gclsrc=aw.ds


The 12.5" Thinkpad X230 has an Ivy Bridge Core i5 CPU with the Intel HD 4000 graphics core, but they sell for above $300. Here's one on ebay for $379.

http://www.ebay.com/itm/LenovoThinkPad-X230-laptop-Core-i5-Gen-3-2-5Ghz-Backlit-Keys-Webcam-8GB-Finger-/121765618676?_trksid=p2141725.m3641.l6368...
It's going to be difficult getting into an 11" model that doesn't have a cell phone/tablet processor in it, especially at the price. I would suggest moving up to a 15.6" with a 4th generation or newer i5. There is also this one with a dedicated card for $279 that should give you higher playable settings than you require: http://us-store.acer.com/aspire-e5-521g-60bx-notebook Though those games revolve more around single core performance, so I would check out a i5 42XX(H/M/U) or i5 5200u if you can find one in your price range.
 
The Lenovo X220 can be purchased for less than $300 at Newegg. However, it only has a Sandy Bridge generation Core i5 CPU which means it has the Intel HD 3000 graphics core.

http://www.newegg.com/Product/Product.aspx?Item=9SIA1ZD3208651&nm_mc=KNC-GoogleMKP-PC&cm_mmc=KNC-GoogleMKP-PC-_-pla-_-All+Laptops+%2f+Notebooks-_-9SIA1ZD3208651&gclid=Cj0KEQjwvo6wBRCG3Zv92ZSLlIYBEiQA5PLVAts1OVV9brq6aSBOcX4ZeidPHFQTcHAym0xkMCESRyQaAsWw8P8HAQ&gclsrc=aw.ds


The 12.5" Thinkpad X230 has an Ivy Bridge Core i5 CPU with the Intel HD 4000 graphics core, but they sell for above $300. Here's one on ebay for $379.

http://www.ebay.com/itm/LenovoThinkPad-X230-laptop-Core-i5-Gen-3-2-5Ghz-Backlit-Keys-Webcam-8GB-Finger-/121765618676?_trksid=p2141725.m3641.l6368



As for the original question... 11.6" laptops with Core i3/i5/i7 CPUs simply do not exist. All 11.6" ever manufactured uses Intel Atom CPUs. The closest would be the 13.3" Dell XPS 13 laptop which starts at $799 for the Core i3-5010u and the Intel HD 5500 graphics core. The thin bezel means that this 13.3" laptop is actually very close to the size of a 11.6" laptop.
 
Solution
No I believe there is ONE Dell 11.6inch Chromebook with an i3-4005U. Correct me if I am wrong. It is probably even in your price range. But, it doesn't have Windows which could be a problem depending in how you look at it.

Edit: I found it, here it is:http://www.amazon.com/Dell-Chromebook-11-6-Inch-Notebook-i3-4005U/dp/B00OW0DTX4/ref=sr_1_1?ie=UTF8&qid=1443146072&sr=8-1&keywords=Dell+chromebook+11+i3
 
Since Intel released the Intel HD 3000 graphics core; which is their 1st integrated graphics core (inside the CPU); each new generation is on average about 15% - 20% more powerful than the previous generation. Actual performance depends on the specific game.

So that means the Intel HD 4000 is 15% - 20% more powerful than the Intel HD 3000.

The Intel HD 4400 is somewhere around 33% - 44% more powerful than the Intel HD 3000.



Below are videos of CSGO being played with the Intel HD 3000, HD 4000, and HD 4400. On the HD 3000 the video shows the settings are a mix of high and very low settings at @1280x720 with only trilinear filtering enabled. The graphic settings for the HD 4000 is not shown, but it looks like everything is set to low / medium. For the Intel HD 4400, the video shows 1366x768 resolution, everything on high graphic settings with both FXAA and trilinear filtering enabled. Not exactly a fair way to judge performance since they are not using the same settings.

https://www.youtube.com/watch?v=WgI6C72eihQ
https://www.youtube.com/watch?v=1UOle1uU_B8
https://www.youtube.com/watch?v=zjsF0RGajR0