Should be a pretty wide range of choices out there. The wild card will be the airline - all have carry-on restrictions, of course, but how they’re enforced varies wildly. Even today, with most airlines supposedly restricting passengers to one piece of carry-on luggage and a personal item like a small briefcase, I see people lugging on enough gear to trek across the South Pole. As a rule of thumb, though, about 3,000-3,500 cubic inches of capacity is the supposed limit to a single piece. That’s not a huge pack, but if you pack carefully you should be able to manage for a week or more of trekking fairly comfortably.
So, then the decision is this: Buy a true backpack that size, or a hybrid travel pack? If you really intend to carry the pack on your back a lot, then I recommend getting a “real” backpack. Mountainsmith’s Ghost 3000 ($190) would be one such pack, as it has 3,100 cubic inches of capacity and a great suspension. Plus, it doesn’t have a lot of straps and loops hanging off it that can snag in overhead racks or in luggage-sorting gear should you have to check it for any reason. Gregory’s Gravity ($195) is another good option, though it’s a little strap happy. But it’s also larger than the Ghost, and probably would be fine around most airports and make the cut as a carry-on. One thing you could do is pack a lightweight duffel bag that the Gravity would fit into, and you could stow it in that should you have to check it.
Otherwise, look into purpose-made travel packs. Eagle Creek’s Switchback Plus ($235) has a total of 3,600 cubic inches of capacity, with a removable daypack that lets you carry two pieces on board, thus foiling efforts to restrict carry-on size. It’s a backpack, or a wheeled suitcase, so it has good carrying options. I have one of the Switchback’s wheels-only siblings and like it very much. But airline travel aside, I happen to think the removable fanny packs and daypacks on almost all these types of luggage are incredibly lame. I also like Lowe Alpine’s Voyageur 65 ($199), which is a first-rate backpack modified to suit the needs of a traveler, with features such as a hefty side-mounted carry handle, a security pocket in the hip belt, and a zip-up cover for the harness. It’s one of the better thought-out travel packs, in my view. With 4,000 cubic inches of capacity, you might bump into space limits if it’s really stuffed, but in most cases you’ll be fine. And it’s really better for trekking than the Switchback, which is skewed a bit toward town use.