Batboard

I have a new laptop with built-in wireless internet. It works good in some rooms, but does not work good in the room I use most often. I do not have access to the wireless router. Is there a wireless repeater or another way to extend wi-fi reception?

There is such a thing as a wifi range extender. Draw upon your Google Fu. Tons of them out there from well known companies at attractive prices.

Wifi range extenders/repeaters are made by just about every wifi router company.
You can get them from $40 to $100

If you run some cabling from your main router to another area or two other areas and put accesspoints there you could roam between them if they all have the same SSID. I do this with my setup at home, and although a little more advanced, I have it that way at my job as well.

Interesting you don't has access to the router.
So does this mean your taking wifi from your apartments or neighbors wifi ?