First time roadtripper partner
Rather than taking a full week, I'd suggest a three day trip closer to your home. A full road trip with someone you've not traveled with before could effectively end the relationship before it has much a chance to flourish. And as you chat online, you might want to take this quiz and make sure you're both envisioning the same kind of road trip adventure.
There are so many cool places to road trip -- I bet you can find a perfect spot within 500 miles of your home. As far as coasts go, I really like the central coastline of California.
Mark