Middle of the country: there are hills, forests, lakes, swamps to miles of fields. I've pitted it against big game in those places and never been disappointed. When you wander outside that criteria, you begin specializing: low magnification, brush. High magnification, long distance varmints: when you factor in size and mass, that small scope makes sense trudging around the mountains. But yes, a fit, excellent shooter capable of humanely shooting a goat over 500y on a mountain hike will already be carrying a heavier 7mm Mag and want a 10x40mm. For comparison, WW2 snipers were using <6x magnification... the soviet PU was a mere 3.5x21 straight tube.
Unfortunately - except older second hand, budget optics are made in the PRC. Simmons used to offer a decent scope that was made in the Philippines... looks like they make crap now. You'll have to do some shopping and look over labels to see. I haven't bought a new scope in years. I'd start looking at Bushnell (some models are still made in Japan) and Burris Signature. Read the boxes and check the scope for country of origin (usually on the bottomside of the turret area.) Japan, you should be pleased; Philippines most likely. Some decent stuff escapes from the PRC, but I'm always skeptical and just avoid it... had a few bad experiences with junk. Leupold doesn't make the VX 1, 2 anymore and the 3HD is just outside your price range. If you get lucky, you might find a new old stock VX1, 2, 3.
Leupold VX3hd just falls outside of your budget: I am skeptical of the cheaper "Freedom" line. I believe some of the Bushnell scopes are still made in Japan, and the Burris Signature might be made in Philippines. Verify though... I haven't bought a new scope in a few years. Bought one chicom scope that flopped, some came on rifles I bought years ago and they were discarded for reliability issues. Vortex makes a Viper HS 2.5-10x44 that is in your budget: I bought one ten years ago which was made in Philippines - a decent optic. Unfortunately it's cheaper now which is dubious, so check. I just avoid chicom scopes for sake of avoiding crap... I'm sure there are some decent offerings, I just don't know what they are.