The new version of the galaxy map, (http://galaxymap.org/dr2) released today, supports searching for stars. You can enter any Gaia DR2 source identifier or Simbad identifier in the search box at the upper right and if the object has a parallax, its position will be shown on the map. The most probable location will be shown with a green cross hair and other possible locations are shown along a light blue line. If Simbad has more information on the object, some of it will be shown in a pop up box, including common names, coordinates, z height, spectrum and absolute magnitude.
Because Simbad includes all the Hipparcos parallaxes, it is possible to search for Hipparcos stars even if they are too bright to appear in Gaia DR2. Simbad identifiers include common names so, for example, you can search for "Betelgeuse".
By default, the Bailer-Jones et.al. distance catalog is used to determine Gaia DR2 distances. You can turn off Bailer-Jones distances to use the simple reciprocal calculation instead (only available when err/plx < 0.2) by unticking the Bailer-Jones distances box..
Currently the Bailer-Jones catalog is only available through the Heidelberg ARI TAP service which does not include the CORS headers that allow queries to be accessed via JavaScript applications. To solve this I am using a sneaky trick involving a NodeJS proxy running on my own server that accesses the Heidelberg service. I hope that remains stable until the Bailer-Jones catalog is available via Vizier (or the TAP service adds the appropriate headers to support client applications).
In addition to search, I've added a display of longitude and galactic plane distance at the bottom left corner that tracks your mouse pointer (not available for mobile devices).