One of my favorite things about of Shavuot is the centuries old custom of staying up all night to learn Torah. One explanation of this custom is that on the morning that the Jews were to receive the Torah they over slept and G-d needed to wake them up! Mystics also believed that on the first night of Shavuot the heavens receive the studies and prayers, thought and of those who are awake. There really is something spiritual about learning Torah all night and then reciting the morning prayer Shacharit at sunrise.
All over the world synagogues and other Jewish organization run all night learning program including special programs for people with a limited background in Judaism. In Manhattan there is a Jewish outreach organization called Manhattan Jewish Experience run by Rabbi (and drummer!) Mark Wildes and his wife Jill. Each year they run all night learning programs for people with a limited background in Judaism. At MJE on the Upper West Side the topic will be The Devil Within: Torah as a Means to Refining our Character and Overcoming Our Demons. At their East Side location the topic will be Freedom and Human Rights: Jewish Views on the "Arab Awakening" and at MJE Downtown it will be A Paradigm of Balance: Jewish vs. Secular.
The programs start at about 8PM and even if you can't stay up all night it will be well worth it to go for a few hours. On the West Side there is a dinner that costs $36 but the rest of the programming is free. Officially the crowd is in their 20's and 30's but all are welcome. There are both singles and couples (married and unmarried, with and without children) involved with MJE. By the way I am turning 45(Yikes!) this month and I feel right at home there.