If you want corals, your going to need much better lighting over them, with the exception of non-photosynthetic corals. That doesn't mean you need to get a big light that covers the entire tank, but from what you have said something like a 150w-250w Metal Halide would be good over a rock pile with corals on a 120G tank. The other problem though, filtration, is going to cost a little $ no matter which way you go. Even the simplest method of using a hang on back skimmer and media reactor is going to set you back a few hundred dollars, and they really don't make a hang on back skimmer rated for a 120G tank so even if you got the biggest one you could you would still be on the low side for a skimmer, but it would still help. You also have flow in the tank to deal with.. 120G needs quite a few powerheads to get water moving around.. 3-4 Koralia 1400s just as a low starting point.
Eels are predatory fish and usually stay in "Predator" type tanks, tanks with big fish that can hold their own and would normally eat small reef fish, corals, and inverts. While is it possible to do everything your saying.. rock pile with corals, eel cave on the other side, an eel would limit your fish selections quite a bit. Usually people don't put predatory fish in with reef community fish, it is one or the other. There are exceptions.. very large tanks, talking 800G+, where there is enough room for all to co-exist, but even then it is normal for small fish to go missing regularly (eel/lionfish/puffer food) if you mix predators with small reef fish, but obviously that happens all the time in the wild also. A person just needs a lot of $ to keep replacing fish, but if a person has enough $ to run an 800G tank, a couple hundred a month in fish probably isn't a big deal.
Off Topic.. is it just me or does anyone else find it a little funny... Topic is named "50/50 idea" by a person that goes by "all_or_nothing". LOL.. no offense.. just found that a humorous.