The short answer is it depends. What year is the Impala? If it's a 2000-2005 they're great cars that run for hundreds of miles with basic upkeep. The 3.4L engine used in these cars does have the occasional problem with a cracked head gasket which can be a fairly pricey fix, but this is not that common in the Impala and otherwise I would consider them a trouble free car. The 2006-now model Impala is a great car, mechanically speaking. The 3.5L is very reliable and gives great gas mileage.
All in all the Impala is a good used car to buy.