DMD2 includes both place searching using the online Google Places API and place search using the offline map database!
The place search dialog include the following options:
If you are just looking for the closest POI of a specific category, then just tap on the icon for that category, the offline category listing will display a list of the closest places matching that category. Notice that you can scroll the categories and there is one for Town/City/Village too.
If you are searching for a specific POI name then use the Offline search, it should find what you are looking for.
If you are searching for a full address, with street name, number and postal code, then you need to be online and use the Online Search – this uses the full power of Google Places (the best place API) and can find based on address or name.