For example I want to find all restaurants that I can reach from my home in 30 minutes. I already have a database with addresses of all restaurants in town. How can I get the full list of restaurants reachable in given time? I also want to have the ability to choose transportation: car, public transport, on foot or any other. Do google, yandex or other services gives such an API? I'm also considering neo4j (http://neo4j.com/) and openstreetmap (http://www.openstreetmap.org/) but cant figure out straightforward solution.
How can I find geo objects accessible from given address in given time?
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Check the OSM wiki on isochromes. It contains some explanation and lists lots of examples.