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?
If you watch lock picking lawyer, you may as well just leave it open. Most smart locks seem to prioritise convenience over security. -possibly check that your insurance is happy with a smart lock.
I'd go with a good quality traditional key lock fitted properly in a good door and frame. Security isn't a single point task, it depends on many things so think like a bad person and do what you can to make your property a harder target than your neighbours.
A good lock on a bad door doesn't work, neither does a bad lock on a good door. Everything needs to work together.
If you're likely to lose your keys or many people need access a smart lock may be an idea, but good probably isn't cheap.
If it's just you and you can keep your keys safe, then I think tried, tested and simple kit is good.
Ultimately though, as ever, it's your risk assessment based on your needs.
This is a high quality lock that will not be picked, either by a thief or a locksmith. Don't lose your keys!
It is expensive but far less than the thousands you mentioned. Of course without armor to prevent kicking down the door, the best lock in the world won't help you, so installing some armor would be a good thing to do.