Actually, Keystone is probably the easiest place in Summit County for parking and base lodge access, now that the "Pika" lot at Mountain House Base (west base area) is free. (The Marmot Lot, at the west end of Mountain House Base, is still a pay lot.) Mountain House is the original base area at Keystone, but with the development of River Run, it is now often nearly deserted. Base lodges ("day lodges") are a dying breed in modern ski resorts. Like Vail, River Run has no base lodge facilities, but the original Mountain House day lodge is still there, and you'll find plenty of room in it.
To get to the Pika lot (at the east end of the Mountain House base village) from the west (Dillon, Silverthorne), drive 1.5 miles past the main Keystone light on Highway 6, and take a right on East Keystone Road. Stay right on Keystone Road (do not turn left, as most people will, into the huge lot at River Run), all the way to the Pika lot on your right. Walk into the village to the Mountain House Lodge, right at the base of the Peru Lift (high-speed quad).
The only problem might be that the Pika Lot fills up quickly on busy days. On weekends, you could miss out by 9:00am, or even earlier. If that happens, just go to the big lot at River Run. From there, you can either fight the crowds in the River Run village, or hop on the free shuttle to Mountain House.
The free Summit Stage is reliable transportation throughout Summit County, although it can be frustratingly slow, depending on where and when you're going. It's particularly good for getting from Frisco to Copper Mountain, where an express bus will take you right into the Center Village. From anywhere to Keystone or Arapahoe Basin, it will get you there, but you'll age a bit during the ride. It may be your least frustrating route to Breckenridge, where traffic and parking can both be nightmares when it's busy.
Have a great time in Summit County!