Net Analyser (Lite = Free) will tell you the BSSID and the vendor of that BSSID.
All you need to know is the BSSID of your access points or if they are from different vendors its fairly easy to tell them apart and know which one you're connected to.
But this still wont tell you which band you're on. Like you I have one 2.4GHz bgn access point, and a dualband bgn/an at the other end of my house. For that I look at the stats in my dualband access point to see which band something has chosen. iOS (this is mostly anecdotal) seem to prefer 5GHz.
(from dave scott Sept 14, 2016-- ) Actually, the Airport Utility wifi scanner shows the CHANNEL used by each SSID, and clicking the little info "i" button at the bottom shows the freq bands corresponding to the channels, so I think all you need is this very handy utility built into the Airport Utility!)