I actually had someone in the bike shop yesterday with that problem. The bike was 1 week old, but he had changed a flat on it and the tire didn't seat properly. There was one low spot in the tire that thumped like that. Spin your wheel and look at the rim between the brake pads. If the rim isn't wobbling between the pads, look at the tire. Spin the wheel and look at a tangent point on the outer edge of the tire. If the tire dips in one spot then that might be the problem. Let air out of the tire down to about 20 psi and see if you can get that part to lift up even with the rest of the tire (compare next to the rim). Pump it up, stopping frequently to push that spot away from the rim until it rises. if it doesn't want to rise, try some liquid soap on the part of the tire that wants to stay inside the rim.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72