I'm a Nuclear Engineer. I worked with a BS as a Reactor Engineer and I am now working with my PhD as a Research Scientist. Nuclear Engineering has a few sub-areas of interest, with the two primary areas being: 1. Nuclear Power and 2. Radiation Studies. A BS who wants to work on the Nuclear Power side will probably work at a nuclear power plant, at the headquarters of the nuclear division of a utility, work for a vendor like GE or Westinhouse, or work in the Navy nuclear area with subs. I may be leaving something out as I'm typing this up quickly. A BS on the Radiation side may work in the same areas, but will focus more so on matters such as radiation shielding, radiation protection, radiation detection, or some other disciplines. At the BS level you see people working as reactor engineers, nuclear engineers, criticality safety engineers, probabilistic risk assessment engineers, systems engineers, I&C engineers, and so forth.
At the PhD level, the work is more research-based. You said that you like physics. Do you enjoy programming? If so, then perhaps an area that would interest you would be working in radiation transport. There are several transport codes used in the nuclear industry. Some are stochastic (Monte Carlo) and some are deterministic. These codes are used in both sides of nuclear engineering. Much of my day to day work involves the use of those codes, however, I have several colleagues who develop them.
Nuclear Engineering also sets you up for some other specialty areas such as Health Physics and Medical Physics. If you have an interest in Medicine, I have a friend who decided to use his Nuclear Engineering degree as preparation for Med School. He is now becoming a Radiologist.
I'm short on time right now, so I'm not really doing Nuclear Engineering full justice, but I hope this was able to help.
Oh, and as for Civil Engineering, the ones I know who have a BS in the area are having a tough time right now with the lower demand (currently because of the cutbacks in construction) and lower pay, but the ones I know with PhD's are doing OK.