ondate page is just the event archive page but restricted to events on the specified day. So you could edit
archive.php (see this first) and include the event map using the function
eo_get_venue_map() (outside the loop you need to specify the Venue ID - inside, you don't need to pass anyting).
It takes a second argument, an array which takes the same values as the venue map shortcode (zoom, width, height etc). (See source)
Alternatively you can create a custom page and either create a custom template file to show 'todays' events, and use the above function to display the map.
Or you can create a custom page and use the
[eo_events] shortcode and use the
event_end_after arguments to restrict to the desired events (they take relative dates like 'today', 'yesterday' as well as 2012-09-25). The shortcode can used with a 'template' to set the output (and so include a map say). See documentation here.
Hope that helps!