Simply install the game on your home PC, then copy the entire Stardew Valley folder onto a USB flash drive.
Chromebooks are more restricted than Windows PCs, but you still have options: stardew valley unblocked portable
The GOG.com version of Stardew Valley is DRM-free, meaning it doesn't require a launcher like Steam to run. Simply install the game on your home PC,
The game and your save data stay in one folder. stardew valley unblocked portable
A portable version of Stardew Valley is essentially a "no-install" setup. Instead of using a traditional installer that writes data to system folders (which is often blocked by administrators), you keep all the game files in a single directory.