Many of the birds you mention aren't cavity nesters, so a nest box wouldn't matter. Probably chickadees are the most likely. If you put up a box for chickadees, of course make sure it's protected from predators with a baffle on the post or pole, especially since you mention cats and racoons. The hole size is 1 1/8", small enough that house sparrows and starlings won't be able to enter. One thing I read is that chickadees might prefer a larger hole to start with, like 1 1/4", and then once they have established use of the box, you can put a 1 1/8" hole reducer on. Much depends on the habitat in your yard and in the surrounding area. Chickadees seem to like the nest box to be on the edge of a woody or shrubby area. A chickadee box might also attract house wrens, so I guess it depends on whether you want to potentially host them or not. You don't mention what state you live in, so I don't know if you have house wrens. Other suggestions for nest boxes could be wood ducks (since you live near water), or even screech owls, which could use the same box as wood ducks. Or, you could try putting up an Owl Shack in the fall. I've got two up, no luck so far with screech owls, but the woodpeckers sure like to drum on that nice resonant box! If you have many dogs and cats running around your neighborhood, then you might not get anything at all. If that is the case, then you might not want to try and attract wood ducks, because they have to jump out of the box to make their way to the water, and would be easy targets for cats.

I had a robin nest in our chokecherry tree in the middle of our yard and between two sets of feeders. The robin was fine with the coming and going of finches, blackbirds, quail, sparrows, etc., in my yard. The pair fledged 3 young robins successfully. BN

American Robins return to the same breeding area they had frequented the previous year. Taken from Hinterland Who's Who Website. Linda

In addition, you don't know what stage of incubation another nest would be in. So, if the incubation periods are messed up, the other eggs (or both sets) still may or may not hatch. I would just leave it and let nature take its course. Robins are robust and able to readily renest after a failed nest attempt.