I'd need to lower the strings on one of my basses at the nut... what tool should I look into for that job?
Nut files - plain and simple. Some will advocate sanding the bottom of the nut, but there are two problems with this. If the nut is curved on the bottom, sanding is really hit-and-miss though it can be done. And you cannot adjust individual string heights by sanding the bottom of the nut. So get a proper set of nut files or wrap some sandpaper around a suitable gauge of string or a properly sized drill and work the slot down to where it should be. You know where it should be, right? And "lower" is not the right answer.
At the risk of being tarred and feathered by the purists, I use needle files. If you take your time and be careful you can get good results.
Not sure if it'd be worth it to me for the 1 nut I cut every 10 years. I'd like to know what people used before nut files. I can't imagine they've been around since the beginning of lutherie. It seems to me that a lot of the specialized tools may make the job easier and faster if you're a pro, but look through a Stew Mac catalog and tell me 94% of the tools can't be replaced with a hammer, chisel and file.
I've used drill bits wrapped in sandpaper of bass nut slots. 320 wet or dry, or there abouts. Not really wrapped, more like folded (not creased), with the drill bit providing support and shape. For guitar nuts, the fold-out variety pack of little files to clean welding tips work. Under $10.
People have been cutting nut slots with needle files before there were nut files made for that specific purpose. You can achieve just as good of a result with a needle file as you can with a nut slotting file, so it is the proper way to do it.