For non locking nut guitars, my favorite locking tuner is the schaller locking tuners that you push the string through the top when your done. Can't give you a model or anything tho. Take a trip to their sight to see all they offer.
As far as the nut goes, I would recommend replacing a plastic nut, but in the mean time, you can get by with taking pencil lead to the inside of it where the strings lie on it. This is graphite, and will smooth it out when the string moves back n forth, also big bends nut sauce can be a huge help. Cheaper then having a new nut installed, (unless you do it yourself) and deffinately a pencil is cheaper then you will ever spend in your life