There is noplace right near the track, but there are some a few miles away. There are a few to the north, but you generally want to enter the speedway from the south, so I'll give you the ones that are to the south.
Big Tree Car Wash, behind the Shell on US 1:
This one is probably the closest and easiest. If you get off the interstate at the Beville Rd/SR400 exit, you just stay on the road for a few miles until you come to US1 (Ridgewood Ave), make a right, then a couple of lights south you will come to Big Tree Rd, which is where the place is. Take the same way back, and make a right on Williamson Ave (shortly before the interstate), to get to the track. You should see signs from Williamson on how to get to the track. Unless it's changed from last year, you'll be making a right at the 2nd light.

These are both on beachside. If you are staying at the event hotel and have directions there, these are located nearby.

Tornado 24-hour self serve carwash, behind baskin robbins on beachside, a little ways north of the Holiday Inn most people are staying at:

There is also one that I don't have the address to, but if you head south and make a right on Dunlawton Ave, right after the burger king, it is just around the corner on Dunlawton.
I mention both since they may be popular, being right near the event hotel.

And the hotel will have a hose and towels available for use as always