I guess this is my favourite district in whole of Riga as it is astonishingly beautiful and easily reachable (10 minute walk from the opera house, for example). Most of these houses were built at the beginning of the 20th century and they served as apartment buildings for the rich German (with few exceptions) families. Now the residents are mostly embassies or councils or other diplomatic entities, yet the feeling there is not uptight at all.
This is a great place for taking a walk in the afternoon, I think. Very calm, peaceful, safe and beautiful. You can also take a cup of coffee at All Cappuccino either on 11 Antonijas iela (iela meaning street) or Vidus iela which are all there and serve really good coffee, nice staff and relatively friendly prices. I reccomend this one because it's the only one I know in the district that I have used myself, but if I will find something better, I will let you know. So for now, enjoy the pictures and see if this is the kind of experience you crave for!