Greensboro is in the Piedmont (central) area of the state. We have "rolling green hills", but nothing too large. The further west you go in our state, the bigger the hills get until you're in the mountains, which are about 2 hours from here.
You can get a pretty decent/nice new construction home in your price range. It will more than likely be a "cookie-cutter" home, but that's not bad if it's your first home. You can always get something more unique a few years down the road.
There's been quite a bit of road construction (and still is) in Greensboro, so I don't think there are a lot of 2-lane narrow roads. It just depends on where in Greensboro you live and how far away from town you are.
The area of town with the best reputation is northwest Greensboro, but western, southwest and southern Greensboro aren't bad, depending on the neighborhood. With Southern Greensboro, the further south (moving towards Randolph County) the better.
You should first check out homes in the 27407, 27408, 27410 and 27455 zip codes. Pleasant Garden is also very nice.
If you want to live away from the hustle and bustle (though it may not be as busy as Reno), check out Stokesdale, Pleasant Garden (as I already mentioned), Climax, Julian, and other small communities in Rockingham and Randolph Counties. You might also like McCleansville (east of Greensboro), Mebane (Alamance County) or Graham (Alamance County).
As you can see, there are plenty of small towns around Greensboro to look into.
Guilford County taxes are higher than those in surrounding counties (not sure about Forsyth County, to our west), so if that concerns you, look outside of Guilford County.
Just a little FYI, the mountains are about 2 hours west of Greensboro and the beach is about 4 hours east. (Probably 5 hours if you want to go to the Outer Banks.) There's plenty of things to do outdoors (hang gliding, llama treks, rock climbing, white water rafting, canoeing, kayaking, cycling, fishing, boating, etc.), so if you're into that, you should enjoy NC.
I wish you all the best.