There's absolutely nothing wrong with taking some time by yourselves to explore the country and buy each other presents in the process. As long as you both know where you're going, where to meet up, and how to get in contact with one another, then there shouldn't be an issue with getting some meaningful alone time abroad.
Take pictures, but get off your damn phone
I'm not here to remind you that this generation spends way too much time on their phones. In fact, you're probably reading this on a phone right now. So, why not break the trend and use your phones for only the important stuff? Directions, transportation, Yelp, and your camera. As far as Facebook, Twitter, and Snapchat: do yourself a favor and disconnect. Are you really going to browse through the Imgur app while in Costa Rica? Disclaimer: I did this.