I don't think you'll need anything too powerful for games like Sims and Skyrim. I recommend the Lenovo Yoga 730, it is a decent device that has a touchscreen that comes to mind. It is far under $2,000, I don't see the need to spend that much. The battery life should be around 6 hours since this laptop has a 4K display, which is okay. The weight is around 4.2lbs which is fairly portable. The i7 processor and GTX 1050 graphics card should be fine for general tasks and light gaming. The build quality is pretty reliable, and the input devices are overall good. The 4K display is touchscreen and stylus compatible.