If you were basically satisfied with the Specialized Nimbus tires, there's also a Nimbus Armadillo with the added puncture resistant shield.

And I'll put in a plug for my favorite reliable tires, Michelin Protek Cross Max. Those are the heaviest and most puncture resistant, and also often the most heavily discounted -- as little as $20 each occasionally, presumably because some folks don't want to ride with tires that weigh 900-1,100 gr, depending on width.

I put 2,000-2,500 miles on a pair over the past year on my Globe Carmel (Alex Z-1000 622x22 front rim; I replaced the rear with a Weinmann double wall rim and heavier gauge spokes) and never had a puncture flat. Even when shards of glass and roofing nails cut through the heavy duty tread it never punctured the shield (which appears to be a yellow fabric). I recently rotated the pair of tires front and back and inspected them carefully -- there were several slashes, and I used tweezers to pick out a lot of razor thin shards of glass and metal, but nothing penetrated the puncture shield. The only flats I had occurred after a year and turned out to be due to the tube extruding through the nipple holes in the double wall rim through the thin rubber rim strip. I replaced that with Velox or Nashbar cloth tape.

But the Michelin Protek Max is lighter, with less aggressive tread, and the same 5mm puncture shield. And they have a new version of their Urban tire with two options in puncture shields. Bike Tires Direct and Amazon often discount these.