ᐅ How to find a property (house/apartment/land) anywhere in Germany?

Hello everyone!

My situation:
I am married with no children, planning to work for another two years and then retire at 57.
I currently live in Cologne, mainly because I work here, but I am not attached to the city. In fact, the (German-speaking) world is basically open to me for my (pre-)retirement.
I have not owned a car for over 20 years and don’t intend to own one again.

Expected finances in two years:

• Assets: about 700,000 euros
• Passive income: 3,000 euros net/month
• Current expenses: 1,800 euros/month (including 800 euros for rent and utilities), meaning if I stayed in my current rented apartment, I would save around 1,200 euros every month.

What I am looking for now is a place to live for the rest of my life, meeting the following conditions:

• Quiet. VERY quiet!
• Shops for daily necessities within walking distance. As I said, no car!
• About 100 square meters (1,076 square feet) of living space. A garden is not necessary, but possible.
• Suitable for seniors. Not necessary yet, but will certainly become important eventually.
• It can also be an apartment rather than a house, as long as I rarely or never hear the neighbors (I know this is hard to predict).
• Not sure if it still needs to be mentioned nowadays, but reasonably fast internet is a must.
• Preferably located either right by the water or in the mountains.

Very roughly estimated, this means I can either:

• Rent something for up to 2,000 euros per month including utilities => I would break even monthly and not touch my assets.
• Buy/build something for a total cost (including moving costs, new furniture, and all expenses related to the property) of 600,000 euros. I want to definitely keep 100,000 euros as a reserve.

Since I do not use a car myself, my first thoughts go towards car-free locations, for example some of the German islands (I am not worried about feeling isolated on an island).
However, a penthouse apartment or simply a quiet location would also be suitable.

My questions:

• How do I find a place like this? The problem with real estate websites is that the searches mostly start with entering a postal code. But I am flexible and cannot realistically search all postal codes one by one. Real estate agents usually work locally anyway.
• When should I start searching seriously? The earliest opportunity to move will be in less than two years, but there is no objection to staying longer in my current rented apartment if circumstances require it.

Thank you!