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;
