Brian - I've looked up and down all aisles of my LA HD for 'the good stuff,' but it just isn't there. There's the 4 hardwoods I mentioned - red oak, hard maple, tulip poplar, and birch - a bunch of douglas fir 2x, 4x, and 6x stuff, some redwood stuff, mostly for decking, trellises, and the like, some variations of pine (knotty, select, radiata), pressure treated, and then random things like doweling and molding. I wish they had just a little more. Even just the addition of walnut would be fantastic, but alas, it really is built around framing and decking, not benchtop woodworking.
If your HD is different, do tell! I'd love to hear about it.
Oh, and I went to Lowe's for the first time last month to help a friend pick up a very large ladder in my truck. I asked if we could troll the lumber aisles, hoping for some finds. It was mostly the same. They had some nicer pine than I'm used to, and I think one other hardwood, like ash, but other than that, it was pretty much not worth the extra mileage to get there. HD is only a couple miles from me. I had better luck with Anawalt Lumber. They had a few rarer things for me, like beech and walnut, but still not a whole lot. It seemed a lot better as a place for parts, like hinges and knobs, bits, gardening supplies, and lots of around-the-house chemicals. They did have a section outside of larger building lumbers, but there wasn't much I could make out beyond the usual stuff, and it was all poorly labeled. My other option is Anderson Plywood, which has lots of fun stuff in large sizes and long lengths: wenge, zebrawood, alder, walnut, beech, as well as all the usuals, and of course, tons of plywoods in real wood and veneer outer layers. This is also very close by, so mostly I hit up HD and Anderson. We don't have sawyers out here in LA - at least, not within a few hours of driving.