Putting the "Find place" box on top is fine.
But "Set Initial Location and Zoom Level" isn't much real estate to lose; hiding it would just serve to make things less usable: more clicking, a more convoluted interface...
If possible, maybe accept both lat & lon values in a single field, to facilitate pasting coords E.G. from popups from the HB or wptedit.
As for the functionality of OSM Nominatim itself, it thinks "Portland" is somewhere in the Pacific coast. Which we all know is factually incorrect. "Portland CT" maps to a road by that name in Great Yarmouth, Norfolk, and "Portland ME" maps to a local road in Hermosillo, Sonora. Oh what, I gawtta type out the full name theyah, Emm Eh Aye Enn Ee? That's a bit frickin' much bub.