I'll bite. I've been to several stops for various chores and a bit of exploring.
Nearby Chuanxin Gulou is a restaurant that sells dog meat on the intersection of Beijing Rd and Doufuchang (haven't eaten there, but kind of an exotic thing some reader might want to do). There's also a walkway market near the bridge connecting to Yuantong temple. If you keep walking to the right there's a neat little street which has older style homes and stores.
Dongfeng Guangchang obviously has a whole strip of shopping malls, but the Holiday Inn with some fine dining options is just a little bit more up DongfengDong Rd near the intersection with Baita Rd and there is a nice little park by the Panlong River.
The Vietnamese consulate is in a building called Hongta Dasha which is near the Huancheng Nanlu Subway stop.
Taking the subway to get to the train station is equally easy from the Huancheng Nanlu stop and the Kunming Huoche Zhan stop because if you go to the subway stop for the railway station proper is behind the station and there is a convoluted path for entry.
Near the Erji Lu stop there are two consulates - Myanmar and Laos.
If you go down to Xinyazhou Tiyucheng obviously there's that whole Xinyazhou Tiyucheng complex but on the opposite site there is a small Yi village called Zijuncun which still has some old and traditional buildings if that is your cup of tea.
Nanbu Keyun Zhan: A massive bus station with buses going to Jinghong, Mengla, Mohan and other places southwest-ish
From Dounan you can go to "Chenggong Laojie" by bus (look for Chenggong Guangchang). Its not quite as close as OP suggested, but its a really neat little old strip of mostly Huizu shops and houses; probably what Kunming looked like 20 years ago minus the occasional speaker boxes.
The universities and couple of government buildings are further south. Also the buses are not so reliable the further south you go.