There are some chains, like rockler or woodcraft that keep some wood in stock, but they are (in my experience) more expensive, unless you need something very small.
I live in Colorado, and there are a couple of stores that specialize in lumber, but AFAIK, they aren’t chains. I think that’s pretty common, and you’ll have to find the dealer near where you live.
Some terms to search in google are: Lumber, hardwoods (although also gets flooring stores), building materials (this is hit or miss in Denver), sawmill.
Chances are, if you called one of these places and they didn’t sell hardwoods, then they would know where to go to find it.
I also really like BB plywood (not the home center stuff) they sell. It’s pricey, but it’s almost like sugar cookie dough when it’s milling.
In Denver, I like:
- The Front Range Lumber Company
- Frank Paxton Lumber Company
- Austin Hardwoods
There are several more that I’ve never visited. I usually go to FR, because they will cut the sheets to fit in my car for free. Austin charges $5 per cut. Frank Paxton has a “Hardwood of the month” where they have some huge amount of one wood on sale each month.
The rough cut stuff is the cheapest, but you’ll need the machines to clean it up (planer, joiner).
There are also local plastic places I’ve found here in Denver, if that interests you. There is a remnant sale at one shop here that has >50% off discounts if you just need something small and are willing to rummage through a box of scraps.