Repeated bike flats

If there is a flat, 99% likely there's a ole, you just didn't see it.  If I had a tube that went flat, I wouldn't put it on even if it looked like it was holding air (I'd perhaps pump it to 120 and leave it overnight, then I would use it if it held up)  Weak tires don't cause flats unless there are holes in them

Did you save the tubes?  Inflate them all, find the holes.  If they line up or are near eachother, you've found the problem.  If they are on the non valve side, it's rim tape, valve side, something in your tire

I'd say rim tape is #1 culprit (see Yanti??    What kind do you have?  plastic?  is it fully over all the spoke holes and intact?  Replace it with velox

Make sure no spokes are protruding through the spoke hole

Double check the inside of the tire to make sure no staples thorns etc.

x2 what Chris said, plus if you feel up to it and none of his suggested troubleshooting shows anything wrong, I am now a firm believer in Armadillo (by Specialized) tires.  Your LBS should sell them for around $40 each.  I had three flats in two weeks, got disgusted, and got the Dillos.  No flats since, and I am a happy camper. 

Small tears in the tire could do it.  You won't easily see them when the tube is defalted but once you pump it up the tube could pop out a little and that will cause it to pop soon after.  I always try to look at my tire after replacing a tube and pumping it up. 

You changed your tire.  Did you get the bead set correctly?

You'll also need to check your rim tape.  It does wear out after a bit.