Can attest to ASUS making good routers, though I got a cheaper one than the AC88U. I bought the RT-AC1200 for $50 and it’s great so far. The only thing is I don’t know if it will reach the square footage OP is looking for. But since the budget is 130$ then they could probably buy some WiFi extenders for around the house.
One of these should work. Plug it in where the signal from the house is strongest.