There is one Hardy's about halfway to the Conrad, from the airport. I'd guess it's $2-3 one way. There is a parking fee of 2-3k IDR. As always you can ask them to wait (standby), and the waiting charge is 4-5 cents per minute. There may be other Hardy's, but that's the closest one I know of.

There is a minimarket near the Conrad, Pepito's (opposite side of street, just before the Holiday Inn Resort) that we found fulfilled 90% of our needs.