Congrats on your purchase! Hope you find them as useful as I do. I always carry several - both the normal Stylus 3 and the Reach models. I buy batteries either at Office Depot or a local drug store with a camera shop that happens to stock the AAAA.
I use them at work for:
Illuminating holes or openings. Since you can jam them into spaces and light them up, I use them for opening up floppy drives, tape drives, Zip drives... prior to cleaning or repair. Leaves your hands free for cotton swabs, compressed air... Regular lights of AA size are too big.
Since they tend to be spot beams, illuminating specific things or pointing out particular pieces. i.e. showing the customer burnt circuits or blown chips. Time to replace the computer!
Dropping them into wallspaces. I do lots of wiring in double-wall construction. I drill a hole at the top of the wall, drop one in on a string - that way I can see what is in the wall. It is so much nicer than cutting into the wall and wondering if you are going to hit a live wire. I used to use a Solitaire, but the cleaner, whiter light of the LED is a plus.