Ok so before I recommend a laptop let me provide you with the Minimum requirements of a PC to run the Sims 4...
Here you go :
PC MINIMUM REQUIREMENTS:
REQUIRED: Internet connection required for product activation.
OS: Windows XP (SP3), Windows Vista (SP2), Windows 7 (SP1), Windows 8, or Windows 8.1
PROCESSOR: 1.8 GHz Intel Core 2 Duo, AMD Athlon 64 Dual-Core 4000+ or equivalent (For computers using built-in graphics chipsets, the game requires 2.0 GHz Intel Core 2 Duo, 2.0 GHz AMD Turion 64 X2 TL-62 or equivalent)
MEMORY: At least 2 GB RAM
HARD DRIVE: At least 9 GB of free space with at least 1 GB additional space for custom content and saved games
DVD-ROM: DVD ROM drive required for installation only
VIDEO CARD: 128 MB of Video RAM and support for Pixel Shader 3.0. Supported Video Cards: NVIDIA GeForce 6600 or better, ATI Radeon X1300 or better, Intel GMA X4500 or better
SOUND CARD: DirectX 9.0c Compatible
DIRECTX: DirectX 9.0c compatible
INPUT: Keyboard and Mouse
So this means that your laptop needs at least these specifications in order to run Sims 4...
The
Acer Aspire E 15 E5-571-7776 15.6-Inch Laptop is a little over $500, but it would be an excellent option for you and would play the sims 3 and 4 excellently.... It has a decent graphics card, excellent processor, nice memory, great storage.. plus a very good battery life..