Combining two fields in a DataTextField. Is this possible?

You can add an additional column to the datatable that is a computed column and use it as your datatextfield (see the Microsoft Learn Multi-field Data Binding documentation page).

So for your example above you could do something like this:

dsAddress.Tables[0].Columns.Add("StreetAndPlace",typeof(string),"StreetAddress + Place");
lstAddressDropdown.DataSource = dsAddress;
lstAddressDropdown.DataTextField = "StreetAndPlace";
lstAddressDropdown.DataBind();
lstAddressDropdown.Items.Insert(0, new ListItem("Please select"));

To add a space between the StreetAddress and Place replace the expression string shown above with "StreetAddress + ' ' + Place"