Every £50 entry level sat nav that you can buy from Halfords will do exactly that. It's exactly what they are built to do.

I'm running TomTom software on a PDA (Mio P550) and it has taken me all over Europe doing exactly that. You start it up and in a minute or so it knows where it is. Tell it where you want to go - you can enter a postcode (I only have the UK postcode database), an address or you can click on a point on the map. It will then calculate a route - either the shortest or the quickest (you choose) and if there are toll roads it will ask you whether you want to use them or not.

If you stray off the route it will recalculate automatically without getting in a strop and with a few free add-ons it'll tell you where just about anything you want is and take you there - stuff like hotels, supermarkets, landmarks etc - including speed cameras. It will do this all over Western Europe, or other places if you have the maps. It cost me £70 for the software (I already had the PDA).

If you decide that the routing function makes things too easy you can switch that bit off and just have the "you are here" moving map bit on the screen. At night or in poor vis you can use that part as a poor mans night vision system. You can see when the sharp bends are coming up on the screen long before you can see things in the headlight.