I have moved to a walkable area and no longer need to have my car keys on me all the time. My landlord has put in a crappy 4 digit combination style door lock, but said I could change it.
What is the best kind of keyless door lock that I can use instead? Ideally one with decent enough security to be as good or better than a key?
Schlage makes a keyless entry lock that isn't strictly "smart" (no wifi or Bluetooth) but is pretty well made and as secure as any common deadbolt lock. I have two and have been using them for several years with no problems. I can't remember the model but they are in the $100 price class and most major hardware outlets have them.
As others have said, I'd stay away from any kind of fully remote lock.