Even the best router has a range improvement that is barely noticeable above that of any good router. Buying a router for "range" is usually a pathway to frustration since you will likely not get the range you expect. As distance and attenuation occur, your bandwidth drops off until you lose the connection. At the extremes, even if you have a router that will hold a connection, the bandwidth may not even be usuable.
Not only that, but Router<->Client is a 2 way street. If your client device doesn't have similar range capabilities, the issue is null.
A good router with cheap Access Points to fill in coverage holes is a much better solution.