I'd like to translate a common sign I've seen around, which says "hate has no home here". My initial thought would be "这里恼恨没有家", confirmed by dictionaries/etc. However, the character of 家 doesn't seem to express the metaphorical idea of "home" to me, at least. I haven't seen a different word for "home", though. Is this sentence properly translated or is there a better word for "home"?
Try replacing '家' with the idiomatic '容身之所'
仇恨 (hate) 在这里 (in here) 没有 (has no) 容身之所 (place to stay)
仇恨在这里没有容身之所 (hate has no home here)
仇恨 (hate) 在这里 (in here) 没有 (has no) 立足之地 (ground to stand on)
仇恨在这里没有立足之地 (hate has no place here)
I believe an English slogan should still be a slogan after it was translated into Chinese.
I would translate the slogan “hate has no home here” to "仇恨止步!" (hate, stop!) - It implies hate is not welcomed, therefore it has no place here.
Some people, religions, races will encourage their fellows to hate other people, just on the basis of their colour or creed or some imagined difference. Divide the world in 'them' and 'us'.
The English is effective because it is an alliteration.
Hate has no home here. = We don't encourage/tolerate hatred here.
In this church/our house/this club we don't encourage people to hate other people.
We don't encourage people to hate others here.
All slogans, for whatever purposes, should be a short, snappy soundbite. "Hate has no home here" does not, in my view, translate well into Chinese because the ideological connotation of "home", "家" is different in both cultures, (as you rightly alluded to), and hence the many suggestions by contributors to replace it.
My suggestion is 仇恨不生根, "Hatred does not take root", which, I believe, is the fundamental concern behind the exhortation that hate should not be allowed to find a home, or take root, where you live.
To extend an existing answer
As I know, the sign "hate has no home here" is placed at temple, church, or somewhere with solemn air, friendly spirit. It might similar with "hate is not belong to us", thus, 家 could not be used in this context because 家 is family only, not with figurative meaning as a community (us). Therefore the meanings of "home" is quite broader than 家 on both cultures.
With other answer including 仇恨: In my opinion, 仇恨 carries a very negative meaning (very hate, even do revenge), whereas "hate" could be translated simpler as 恨 is enough.
Besides that, a slogan or idiom we might avoid to translate it directly, finding some similar 成语 could be accepted, like this 雪恨消灾
雪恨 - Freeze hate
消灾 - Dissipate disaster