Old Town Edinburgh
Edinburgh is simply packed with history, it will be impossible to absorb it all in one trip. The town is very walkable, both in the new and old sections, though some cobblestone streets can make it a little hard on your feet. Plenty of shopping around if you get tired of all the free museums for every taste. Most of the dining is limited to pub fare, though they do that very well. You could spend days in this city and not see everything, and it's all very charming.
Insider Tip:Take the free tour by Sandemans NewEurope, it's worth it and will show you all the highlights, filling in stories of history and legend, and point out many of the places you can visit (all the museums are free) more fully later. MacBackpackers tour of the highlands up to Loch Ness is also a very good deal if you want to see more of Scotland outside of the cities.