That shouldn’t be a problem; most pack makers have several models that fit up to about 22″, and $250 or under is a perfectly reasonable price for a backpack. Unless you’re regularly carrying more than 40 pounds, in fact, that’s probably all one needs to spend.
One of the champion packs in that size and price range is the Lowe Alpine Contour IV. It’ll hold up to 6,000 cubic inches, depending on how you configure the storm collar at the top of the bag, has a better-than-average suspension, yet costs a mere $229. Hard to beat without spending another $150.
Another really intriguing pack is the new Kelty Mystery Ranch Bigfoot ($250). It’s one of the first Kelty packs to take advantage of the suspension design licensed from Dana Gleason’s Mystery Ranch pack company. Gleason, of course, was the founder of Dana Design, and has long been among the more innovative thinkers in the pack world. The Bigfoot is a nice pack with 5,200 cubic inches of capacity, top-loading design with panel access, provision for a hydration system, shovel pocket, and two accessory pockets. Both the Lowe and the Kelty should fit you nicely.
Finally, for just a bit over your target= - $260 - you could get a Gregory Shasta. That’s really a nice pack for the money. It has 5,300 cubic inches of capacity (in size large), a great suspension, and is made of super-tough materials. It’s one of the better buys on the market - a high-end pack at a midrange price.