Just the experience of being in a place dedicated to firefighters was awesome in itself. The old buildings and ambience of the place was amazing. As far as your weekend...
Organize the in between weekend with some of your classmates. I did the two times I attended the NFA and did Washington DC on one trip, spending the night and taking in all the sites and the other time drove to Jamestown and the surrounding area. Remember to bring a patch for the Otts Bar which is located off campus. Firefighters put their departments patch on the wall at the bar. Pretty cool. Enjoy and learn. The whole experience is a must for all firefighters during their career.
Have been to NFA 8 times going back in Oct 2011 for 2 weeks. Some of the best training I have been to in 30 years of service.
You can go to DC on the weekend, you could also go to Baltimore or Philadelphia. Gettysburg in 10 minutes aways you can see after class or spend the weekend there.
Make sure to go be Emmitsburg FD. And the Command post on campus, some of the best learning takes place there after class.
Enjoy your time there and try and bring a friend with you.