Extract certain geodata from OSM File

You can do it but it is not trivial. The easiest way is probably importing the data into a PostGIS database with osm2pgsql (you can make it import only the features you are interested in) and then work with SQL. Thing is that the "parts of town" you're after may be mapped as a single node (place=suburb or place=neighbourhood) in which case they have a straigforward lat/lon, or they might be a polygon in which case you need to compute the centroid (which is easy to do in PostGIS).

I am not sure what the status of osm-to-mysql importers is. I suspect it will be easier for you to get to grips with PostgreSQL than to try and import to mysql - the difference in terms of SQL should be minuscle. Of course you can compute the centroid for all parts of towns in PostGIS, something like

SELECT 
  st_centroid(way) AS geom,
  name,
  place
INTO
  ortsteile
FROM 
  planet_osm_polygon
WHERE
  place in ('neighbourhood','suburb');

After that, add those that were already present as points

INSERT INTO 
  ortsteile
(SELECT way as geom, name, place FROM 
planet_osm_point WHERE place in ('neighbourhood','suburb');

You might also want to add the admin boundaries on levels above 8 to the mix. And later to find out which city something is in,

ALTER TABLE ortsteile ADD COLUMN ort VARCHAR(64);
UPDATE ortsteile
SET ort = (SELECT name FROM planet_osm_polygon
  WHERE boundary='administrative' AND admin_level='8' AND
  st_contains(way, geom));

Because in Germany some cities ("kreisfreie Städte") have an admin_level of 6 you will want to re-run the last query for those points that didn't have an admin_level 8 parent:

UPDATE ortsteile
SET ort = (SELECT name FROM planet_osm_polygon
  WHERE boundary='administrative' AND admin_level='6' AND
  st_contains(way, geom)
WHERE ort IS NULL;