One of my favorite knives is the Benchmade 770, which is right around 2 2/4" - it's nominally 2.80", which is a few thousandths of and inch over.
While it's not in your $60 range, if that's your favorite size, keep the 770 in mind for when you want to spend a little more on a first class knife. It's a great gent's knife, and came in enough versions - carbon fiber, G10, different colors of Aluminum, 154CM, D2 - to please a range of tastes.
The bad thing is it's out of production, and only going to get more expensive. But there are still enough of them around that they can be picked up for reasonable prices, which probably won't be true in a couple years.
I'd also look at AG Russell - he has had a number of folders in that size over the years. Some were quite expensive, but some were very modestly priced.
Meanwhile Benchmade's 'NRA Knives' line has a couple of folders with 2.72" and 2.80" inch blades. The 12410 retails for $80 (so it streets under $60) and the new ones are in D2 tool steel; the 12750 is a whittler-ish three blade folder with a locking 440C main blade and no clip, and full retail is $55, so it runs around $40 online. They're both mini versions of Ken Steigerwalt designs. I own both, and while they aren't as incredible as the 770, they are solid, well built little knives. The 12410 is a great drop-point cutter, full flat ground; the 12750 is a bit thick edged but has one of the stoutest spines I've ever seen on a traditional-ish multiblade folder, it looks damn near an eighth of an inch (it's a nominal 0.100"). Its second blade is a very thin edged semi-skinner, and the third is bottle opening screwdriver. Sort of a low featured Taiwanese Benchmade SAK.
