Low budget Panasonic LUMIX DMC-FT30, otherwise Panasonic LUMIX DMC-FT5 or Olympus TG4.
FT5 offers best image quality of the three, wifi-control, 'manual' control and long exposure (15" and 30").
TG4 offers wifi-control, 'manual' control, raw in some modes and Live-Composite. The last mode is nice for light painting, as you can follow the results on the screen and add more light where needed.
FT30 is just a basic camera which will do the job, but some people might not be happy with the image quality which is still better than Ricoh/Pentax WG-series in most cases.