Marty, you might want to check either the Garmin Nuvi 370 or 670. Those models are equipped with both North American and European maps, and are available for about $375 or so (for some reason, the higher end 670 is priced below the 370 at the moment?). Check the current prices and description at Amazon.com.
I'd suggest buying a GPS unit rather than renting it, as you'd be able to use it not only on future trips, but also for domestic travels.
I've been travelling with a Nuvi 370 lately, and it's really helped on a couple of occasions. However, the routing it chooses is a bit unusual at times, so I'd suggest taking a Michelin map as well (always wise to have a backup!).
Happy travels!