I'm in complete agreement with the above two posts.
I'm also a bit confused . You say you have 4 nights to do the journey but then talk about 2 nights along the journey and the third night in Inverness. What has happened to the 4th night? Do you mean four days ? Remember 2 nights may only give 1.5 days in a place which isn't long.
What is attracting you to Inverness? Loch Ness is not the most attractive of the many Scottish Lochs - there are better and Nessie is a tourist fuelled myth.
What are your plans after Edinburgh as that may well influence further plans and help given.
Assuming you have four days then York, Durham or Alnwick areas would make the most sense and it would be very easy to spend the full time in just one of these places.
York has the Minster (don't miss choral evensong), walls, castle, very good museums and some lovely countryside around it. Day trips to Castle Howard, North York Moors spring to mind, with the ruined Rievaulx Abbey, the ruined Pickering and Helmsley Castles and even a trip from Pickering to Whity on the North York Moors Steam Railway!
Durham has the cathedral and castle and walks along the river banks. Access to the Durham Dales (Teesdale or Weardale), Hadrians Wall and the wonderful Beamish Museum (which easily fills a day- or even 2!)
Alnwick - Castle and gardens, Bamburgh Cstle, the ruined Warkworth Castle, Cragside (described as the house where modern liviung began), boat trip to the Farne Islands, drive across the tidal causeway to the Holy Island of Lindisfarne. BUT do check tide times for crossing as the sea comes in very quickly and vehicles regualrly have to be rescued from several feet of sea water.