I actually grew up in the Bronx on Loring Place (near the Fordham Road area). I always thought there was plenty to do: The Bronx Zoo, the botanical gardens, and, let's not forget, Yankee Stadium. There's Orchard Beach for summertime fun! I learned that there is the BCA’s Bronx Culture Trolley Program on the First Wednesday of each month (except September and January); and since the Bronx is the birthplace of Hip Hop, there are now Hip Hop tours! There are movie theatres and shopping. Transportation is a cinch with the trains and buses. There are art galleries galore! Go to a symposium at Fordham University and listent to a great lecture, or even better, take a course or a whole program at Fordham U. I love the Bronx. No matter where else I've lived, the Bronx has always been home to me. I found a good link for you: http://ilovethebronx.com/?pg=home.
And if you're tired of the Bronx, there's always the #6 train starting at Pelham Bay into Manhattan.