Strictly from a financial point, rent the car. All the non-financial considerations, e.g. convenience, are just icing on the cake.

You'll probably spend at least $30 each way for cabs to the airport, so at $100 for the car for a week, you'll spend around $5 a day for the convenience of having the car. Go to Seraphina, Simply, and perhaps a dinner out one time, and you're ahead of the game.

Sure, you can do without, but I don't think it's worthwhile.

ETA: I just noticed this is a short trip. My conclusion still holds.