You can stay in either Sidney (Days Inn, Holiday Inn, Econo Lodge), or Piqua (Comfort Inn, LaQuinta Inn). Eateries, and shopping are close by in both towns.
Both Sidney and Piqua, are 1/2 hour or so from the track.
Plus, since the opening weekend in a 2 day USAC show, a lot of the racers stay in the hotels in Sidney and Piqua too
Normally, on Saturday about 9:30-10AM or so, the guys roll the cars out of the trailers to begin maintenance. You get to really check out the cars, the trailers, talk to the crews, and a lot of times the drivers show up too...autograph time
Most times they will fire the cars down the street in Sidney, and in the parking lot at Piqua.