Look in places where the city centre is more than 650 years old, hasn't been carpet bombed in WW2 and wasn't popular enough to be replaced by modern concrete or glass&steel highrises.

You will find hundreds if not thousands of towns in Europe with whole streets full of 13th/14th century timber frame/fachwerk houses in the city centre.

There are also dozens if not hundreds of 12th/13th/14th century stone bridges still in use - usually such bridges didn't fall down, but were taken down and replaced with bigger and better ones as cities expanded.

Though ultimately the only reason to keep around old bridges or houses - just like churches - is nostalgia. The modern version could replace the old constructions at very low costs and with much lower maintenance and better comfort characteristics. Like antique cars, it is the quaintness and historic significance that keeps them up rather than their actual infrastructural superiority.

I think you're underestimating the aesthetic value of older structures. Quaintness, nostalgia and historic significance are all slightly cheap-sounding reasons, whereas the value of artifacts/structures as aesthetic production is impossible to dismiss.