Our wifi is not reaching all rooms in our house. Our neighbor just got a new router and that has made a difference. What do we need to do to do the same?

Not necessarily. You can keep your router and add a wireless extender. A better router might be an option too, but is not the unique solution. Also, if your problem got worse lately, you might be using the same channel as a neighbor. Get a wifi scanner app and see if the channels you're using are also being used by more powerful routers nearby.

Get a new router

You're only going to receive answers from Google users nobody from Xfinity. But as Wi-Fi signals are heavy best bet you can do with your current router is place it high up in your house otherwise contact the store to see if you can get it updated router

Yes, it is the best option