.....it can lead one to do some very silly things. Taking US 60 west of Richmond, VA, followed by a series of slightly glorified goat trails to US 460, thence US 460 through Roanoke to I-81 is one of those silly things Google Maps would have us believe is a good route. I've no doubt it's the SHORTEST route, but it's an awful choice, especially in an RV.
And of course I don't know if you actually contemplate following those directions exactly, Michael, but if you're looking for the fastest route between Washington, DC and Nashville, TN, this isn't it, and it's not even close.
I would assume you're planning to overnight near DC on the 30th and drive all the way to Nashville on the 31st in order to celebrate Halloween there. Mapquest says DC-Nashville is 665 miles, somewhat in excess of a recommended day's drive distance from the general consensus here in the RTA Forums. Be that as it may, getting over to I-81 in NORTHERN Virginia is your best bet, unless your RV Park on the 30th is on the south side of DC. If it is, rather than fighting your way to and around the city, headed in with the morning traffic to catch the Beltway around to I-66, continue south on I-95 to VA 3 at Fredericksburg, west to VA 20, south to Orange, VA to pick up US 15. Ignore the temptation to take either VA 20, VA 231, or VA 22 towards Charlottesville, and stay on US 15 south to I-64 at Zion Crossroads. I-64 will take you past Charlottesville, over the crest of the Blue Ridge Mountains, to I-81 at Staunton, VA.
A few words about RV-ing around the cities: You may be assuming public transportation will spirit you from RV parks into the cities, but that may not be the case. I know little about urban mass transit, but I'd be a little surprised to learn there is many choices from an RV park into Philly, DC, or Nashville. You'll probably have to cab in and back out again. The DC area has the "Metro" light rail system and perhaps you can find an RV park somewhere in the Maryland or DC suburbs which is on the Metro line. At Nashville, I recall seeing an RV Park along the Briley Parkway, adjacent to the Opryland complex, and with +3,000 rooms at the Opryland hotel, surely there are bus lines/shuttle services from there to "Lower Broad", where the bars and live music venues are, and where presumably the celebration of Halloween is focused. The point is this: You might want to look into the specifics/mechanics of accessing the cities you plan to visit from RV parks before you assume access will be simple, or cheap. RV parks themselves aren't cheap, for that matter. I would expect by the time you pay for the additional cost of renting an RV, overnighting in commercial RV parks for a few nights, buying extra fuel, and paying for several nights' transit into the cities and back out again, you'll end up spending considerably more than you'd spend, for example, renting a minivan for the road travel and finding/piling in to inexpensive motels close to mass transit lines or within a short cab ride of the urban areas you wish to visit.
The "on the highway" aspect of RV travel is a lot of fun. The logistics, sometimes, not so much. Oh, and by all means, plan on purchasing a US Highway Atlas (Rand-McNally makes a fine one and they retail for around $25) either before your trip or immediately upon arrival. There is no complete substitute for a good map and the ability to use it. The atlas will be worth the price paid if for no other reason than to see the odd and often humorous place-names across the South. Right here in central NC, for example, we have the crossroads communities of Frog Level and Lizard Lick.