It's an interesting question. (1) “City A is an exciting place to live, but….” Q: Can I write “... an exciting place to live IN, but...”? A: Yes, it's possible, but not necessary. Q: If “I live in City A.” is right while “I live City A.” is not, why is sentence 1 without "in" right? A: It's to do with the word 'place'. It seems that 'place' functions a little bit like the adverbs 'here' and 'there', in that it doesn't need a preposition with this construction. Here are some similar examples with 'place' - It's a nice place to go. It's a hard place to work. It's a good place to study. It's a convenient place to start. (2) “City A seems like a better city to work IN than City B.” Q: Can I write “... a better city to work than...”? A: No, you can't. You need the preposition. Some more examples: He's a good boss to work for. It's a good point to start from. They're good people to spend time with. It's a good school to study at. It's a good rule to live by. ... and so on. As you can see, you always need the preposition - whatever the preposition is - unless ( it seems) that the subject is 'place'. I'm not sure why, though.