Saigon is a city that can be enjoyed during day time, but that it has to be visited after dark, too. During the hot season, you will find it hard to walk around the city, for this reason I recommend doing as locals do. Wake up early, and when I say early I mean it -- 6 am? --, have a good breakfast and visit the city till 11-12 am. Have lunch, go back to your hotel and sleep or rest till 3-4 pm. Visit the city during the afternoon, have dinner, and walk around the city afterwards. The city is pretty safe. Unless you go to the darkest and smallest streets in an unknown district, you should not be afraid. Most monuments are illuminated by night. A great opportunity for photography enthusiasts.
You already know the building in the picture, don't you? Yes, it is the City Hall.