I have a lower spinal injury in the L5 area, and two at C3 and C4. When injury first happened I went to a sports doctor, one of the top in the country. I learned a lot from him. And he had me using wieghts in no time. The key is knowing what machines to work out on, and how to use free weights without hurting your back, but yes it can be done!
As for something sporty to do.... this is what I did. I bought myself a Mt. Bike and I had it customized. I had a riser bar put on it so that when I sit on the bike in my ride position I am not hunched over nearly as much as a regular position would place me. The straiter my back the safer it is for me in regard to my back. I also made sure that I got a bike that was fit for me. I had a shorter span so that my reach was not a issue either. So for me that put me in a 17 frame instead of a 18 or 19. I bought at my local bike store so that my individual needs, the quality of the bike, and any future work I needed would all be done appropriately. They know how to fit you to the bike and tell the guy flat out you have a back injury but still want to ride, he can hook you up!
I also added a rack in the back with saddles bags for gear and what not. I have a Trek and my first bike was a Gary Fisher which I have to admit I still miss dang it.
I ride trails that are rated a 1-2 and it is ok for me if a few parts are 3, but I never venture on a 3 or 4 because that would not be my fitness level, good back or not lol.
It is fun, great rush at times, but most of all it lifts my spirits just being out there. A lot of places are now turning their old train tracks into "Rails to Trails" and bikes are welcome, and the ride is great. The fitness is unbeatable, and the fact that you can ride at your pace is great too. You can even find local bike clubs that will ride basing groups on their levels, and rides are all told a level before hand, so you can plan accordingly. Well I hope this helps. If you want help finding your area info. PM me and I will help you out.
Taylor
PS whoever said don't ride out doors, I have to disagree strongly with them! Just get the right bike, and the right size, and check out your path, trail, road whatever.