My home sewage system all goes out my property on the west side of the house towards the road. My basement is in the middle of the house and has a drain. There is usually always a puddle of sewage in the road near the curb at the east end of the property. The road its self in front of our house has Many cracks and repairs. This summer, the city patched the puddle area, and it is now back. I sit on a large corner lot. When the city was patching, they looked at the drainage before and after the puddle area and they were free of clogs. It appears to be worse when it rains.

My cousin told me to put this drain stopper in the basement to prevent it from coming up, is this OK will it work and will it come up my toilet if I do this?

Please help. I don't know if this is my issue or the cities issue and if it is mine, what type of expense are we talking about?

Sound like you are talking about the strom drainage system, not the sewer system. Big difference.
Sounds like your basement floor drain goes into the strom drainage system. Your toilet will not be on the storm system.

Let's stop that back up. They make a Flood Guard for floor drains, (see image, Check them out at, Flood Guards For Floor Drains - check valves to prevent flooding (http://www.plumbingsupply.com/floodguard.html) Good luck, Tom