We are doing the 8-day Best of Ireland tour in October and would like to spend several days in Scotland after. Haven’t firmed up our calendar just yet, but maybe 4 days or so. Realize it’s not much time, but would love to get some direction. Maybe someone else has done some post-tour travel after RS Ireland.
Work through Steves' guidebooks for those areas. Your local library will have copies and watch some of his travel DVDs for the same area.
I would suggest flying into Edinburgh. There is plenty to keep you occupied for several days, including the Parliament building, the castle, walk up Arthur’s Seat, see the Royal Mile and visit Britannia berthed at Leith Docks. If you want countryside, look for a Rabbies day trip. Other easy day trips include Glasgow or Stirling.
I agree with the recommendation for Edinburgh. If you have fine weather and decide you want to see a bit of the country side, you could take a train to Dunkeld and Birnum and go for a walk along the Tay in Birnum Wood. Check out the Cathedral and have lunch at the Taybank. :) Or you could fill your time easily in Edinburgh. I too recommend the parliament building tour. If you have an interest in science, the Dynamic Earth is great. If you have been to field and science museums in the US it's fascinating to get Scottish examples! Lots of famous geology in Scotland. Also, the Georgian House in Newtown is delightful. The Yacht Britannia was an interesting and fun tour.