Back to the CB125, Honda stopped importing them to the US in 1985. I'm not familar with where they are sold now, but I wouldn't think it would be worth it to try and gray market such a bike into the US. It's an Okay bike, but nothing special.
The only new street-legal non-scooter motorocycle sold today that's in this very small size category that I know of is the Kawasaki 125 Eliminator. I know nothing about it, but I was never very fond of the small cruisers when I taught MSF classes (perhaps because my knees kept banging into the handlebars when doing tight turns). I just never found them very much fun to ride.
If you're talking about a bike that you're actually going to ride over long distances and in the states, a 125cc bike is awfully small. It's totally tapped out at 60 mph. I'd instead look for a common, everyday, used 200-250cc air-cooled single of the most recent vintage you can afford that has been well cared for. For a Japanese bike of this size, brand/model isn't very important, but condition is. Certainly $1000 or so would get you a decent machine and you could spend less if you can tinker some and fix minor problems.
You know, Honda has made a great little 250cc twin runabout called the CB250 Nighthawk since 1991. This is a slick little bike and I bet you could find a decent older one for $1K or so. It's a twin so it makes a little more power and is much smoother than the singles. While not a dirt bike, it would go virtually anywhere, be bulletproof, reasonably comfortable, and cruise at 65mph getting 65 mpg.
This thread might be of interest to you.