Re: What tuners? And what guitar? 2 questions
+1 to everyone about nuts in general, but another +1 on the GraphTech nuts. The difference is significant.
While locking tuners aren't necessarily the golden ticket, I've found they do help. But, first get the nut fixed.
I got a set of locking tuners installed on my Squier Teles - they already had GraphTech nuts - and the amount of abuse they'll take without going out of tune surprises me still. I love to bend and really abuse the low E a lot, sometimes on purpose just to see if it'll go out of tune. Maybe I need to tweak a couple of percent after I do that. I went a whole band practice (about 2 hours) without having to adjust anything the whole time. I checked after the first and second song, then just forgot the rest of the time.
Part of that, I'm sure, is a proper setup. Once the nut's good, you need to balance the string/neck tension. I'm ok at this, but a good tech will get it right.