Try the Hall of Valor Museum at the New Market Battlefield Park. It is run by the VMI Alumni Association and it honors the VMI cadets who fought in that battle. There is another, private and commercial, museum on the entrance road to the Hall of Valor, but I cannot speak for it as I have not been into it. While you're in New Market, go to the Southern Kitchen Restaurant for some really good regional cooking. It's on Rt. 11 on the South side of the town. New Market is at the junction of Rts. 11 and 211. 211 comes in from Luray to the East of New Market. I-81 runs just to the West of the town, between it and the Battlefield Park. From Massanutten, you would go into Harrisonburg and get onto I-81 and go North to New Market.
Also, just off of Rt. 29, somewhere around Ruckersville, there is a great German restaurant on the West side of Rt. 29. I think that its between Ruckersville and Charlottesville.
If you get as far afield as Lexington, you might want to visit the museum at the Virginia Military Institute. It is a very interesting place if American, and especially Southern American, military history interests you. Lots of things about Thomas Jonathan (Stonewall) Jackson, who had been a professor at the Institute, are on display including Little Sorrel, his horse the last time that I was there. You can also walk over to Washington & Lee and go to the tomb of Robert E. Lee and pay your respects, should you be so inclined. While there, the Southern Inn has good, if expensive, food.