seems vs. seems to be vs. seems like

I've noticed that “seems like” is the most commonly used phrase out of the three.

If I were to say that Los Angeles appears to be a nice city, would using any of these three phrases work because “to seem” means to “appear to be”?

  1. Los Angeles seems a nice city.
  2. Los Angeles seems to be a nice city.
  3. Los Angeles seems like a nice city.

Solution 1:

1.Los Angeles seems a nice city. (This is incorrect. You can't use a noun if you don't use 'to be' in this structure)

2.Los Angeles seems/appears to be a nice city. (Both 'seems' and 'appears' can be used here.)

3.Los Angeles seems like a nice city.(Only 'seems' works here)

'seems'/'appears' + adj. = It seems/appears nice.

'seems'/'appears' + to be + Noun phrase = It seems/appears to be a nice city.

'seems' + like + noun phrase - It seems like a nice city.