You are going on vacation with no checked luggage? Knives are OK in checked bags. I understand the desire to not checks bags with extra fees and potential theft. But you might consider checking some less important and bulkier items in a bag along with a knife and other items not OK for carry-ons: I always pack a liter of water to have in case arrival gets messed up and I am stranded or checking in very late at night; plus I like to have other toiletries and first aid items, sewing kit, etc. I've traveled quite a bit with a handgun and ammo and a couple of knives (according to destination laws) in checked bags and never had a problem with theft. Reports of baggage theft seems to be much worse through Chicago and maybe a few larger cities, so I always try to go through and arrive at regional airports if possible and definitely stay away from Chicago. Denver has never been a problem for me and I can't recall any theft scandals there.
Another option is to mail your knife to your destination and mail it back home, insured. Cheaper than buying even a low cost knife.
To answer your actual question, I assume you are talking about a sturdy folder rather than a sheath knife. If it is throw away and picking it up there, then you are limited to what is available locally. That probably means Gerber, Buck, Schrade, or some no-name Chinese knife for under $30. If available, I have found the Kershaw knives to be pretty well made and many models under $30 (Chinese). Kershaw uses a "flipper" for quick opening but the blades are generally 3" or shorter. For a heftier camp utility knife Gerber or Buck are probably more likely.