Chris
Mighell Street was (and a small part still is) in the Carlton Hill area, probably less than five minutes walk away from the centre of the Kemp Town area. Most of it was where the American Express building is now located, but a small part still remains just to the north.
And most of the other places mentioned (Brighton Place, Marine Parade, Albion Hill, The Level) are all about the same distance away, easily within a "five or ten minute walk" radius.