If you do head out on a date, make sure you bring some roses and a bottle of wine (depending on how well you expect the date to go). If you've really thought ahead, you can bring a Romantic Picnic Basket, or you can shell out for a regular Picnic Basket, but otherwise, it's probably just best to have a snack of Delicious Chocolate Cake (it's guaranteed to make your date Very Happy).
Like I said, cute. Spending the time together with friends is what the game is all about anyway, and there's nothing wrong with taking some time to experience the world and hang out with each other. And if that's a little too boring for your tastes, maybe you can have your date tag along with you to some 2v2 Arena matches afterwards. Nothing gets the romance going like a little bloodshed.