Are you looking to send cable TV to 3 other locations or internet access?
Actiontec makes some wireless transmitters for TV signals. However the signal transmission distance is somewhat dependent on the environment. The newest actiontecs are 1:1 meaning 1 transmitter to 1 receiver the older ones work 1:many (1 transmitter to many recievers. The limitation to this is that they send 1 channel only so whatever your tuner in the basement is set to, that is what every tuner would recieve.
If you are looking to adapt coax for rj45 connections, google MOCA. An adapter won't work for this but there are converters which do.
However, if you have internet in the basement and all you want to do is move it to another floor, network over power adapters are more reliable and faster.