Well I have seen quite a few cases of people leaving Karachi and moving to Lahore, Islamabad or other cities. Trust me I have hardly met anyone who has lived in Karachi since his birth there and liked other city a lot more than his birthplace. Many of my acquaintances moved back to Karachi after living some time in other cities. They all thought that life would be better there but that wasn't the case. There's however just one person whom I know who moved from Karachi to Lahore and was quite happy there.
The thing is once you get used to living in a big city, smaller cities no matter how good they are on their own won't attract you, unless you want to live your retirement life which is altogether a different ball game. Same goes for people who live in a big city abroad, they find it difficult to come back and live in Karachi, Lahore or any other city.
I am myself from Karachi but have moved a bit in my job. I have lived in Lahore for 5 years at different places there and recently returned back to Karachi. Have lived in Islamabad too for a short period. Lahore has different set of problems, as do Islamabad, just like Karachi has its own issues. I am happy to be back in Karachi even though I am really frustrated with some of the negatives here which are quite obvious (detailed well above) but i'm happier here because of following good things:
- A lot better accessibility for almost everything you need. Anywhere else you go, you would find it difficult to adjust to the fact that you would have to travel a lot or compromise due to lack of availability of the thing you want to have.
- Better career prospects and opportunities.
- Higher professionalism.
- Quality goods at comparatively cheaper prices in general, except rent and cost of house/apartments.
- Food!!! Tasty and a lot of variety! - can't stress this more.
- Shopping at night time and the fact that you can roam around at 2 AM and everything is open (sorry Islamabad!)
- Lesser loadshedding of electricity and gas. Water problems however are a headache here.
- Better weather all year around as no extreme Heat that you can't survive without AC all the time or can't go out, and conversely so cold that you can't survive without heaters shivering you way trapped in home.
The thing is grass is always greener on the other side and we humans have an in-built trait of taking things for granted - only realize their value once they are gone, which happened in my case when I moved away. Happy to be back.
P.S. Just saw from your post above that you are from Sindh, relatively new to Karachi as well and desire peace.... Well in that case you can consider Islamabad - although it's very expensive.