But if you built a similar city it would likely have high prices too. Why not try to get more housing built in the places that are already nice instead?
I'm not sure I understand this, why would walkable places be expensive? Walkable places are generally high density which means that buildings are bigger and homes are smaller so prices should be lower.
That sounds like a fake supply problem. Potentially people having places to sell or rent blocking high density developments, or lack of infrastructure causing issues.