I have returned from my trip and wanted to give a recap and say thanks for the suggestions. Edinburgh was absolutely amazing. Such a cool city. I ended up staying in New Town, which was cool but I was always walking over to Old Town to do stuff. I did the castle and saw the one o'clock gun, the scotch whiskey experience, greyfriars kirk, hiked to Arthur's Seat (awesome), Holyrood Palace (meh), the Royal Mile, and the National Museum, which I could have spent all day in. I was there for four nights and spent two of them at an awesome pub on the mile called The Tass, which had really good folk music both nights. I also took a tour one day to Loch Lomond and Stirling Castle. Lomond was a disappointment because it was snowing and you couldn't see anything, but Stirling was pretty cool. I spent half the time looking down on the Stirling Bridge battlefield and imagining what it was like.
Overall a very satisfying trip. I'd really like to go back in the warmer months and see St. Andrews and more of the highlands. I was also pleasantly surprised by the number of quality women I saw while I was there. Thanks Pit!
ETA: I also did a ghost tour that was highly disappointing. Want my money back.