I grew up in St Leonards and lived there for over 20 years. I moved away and would happily never visit again if I didn't have family there.
I'll give you my honest opinion - houses are cheap for a reason. Like a lot of seaside towns, Hastings/St Leonards are very deprived, and there are lots of problems with the area. It's nice to go to for a sunny day at the seaside, and yes the houses in the more upmarket old town area are nice, but that's where the postitives end.
Crime/violence is getting worse, and there are some areas I would never walk around at night including St Leonards Warrior Square. I actually felt genuinely threatened on the occassions I had to walk back from the station after 9pm. Even during the day you have to be on your guard.
If you have kids, don't even think about it unless you have the money to go private. All the secondary schools in Hastings are beyond awful, with abysmal GCSE results, and even those in the surrounding areas are not much better unless you can get into a religious school. Some parents pay for their children to travel to Battle or Robertsbridge, but spaces for these schools are sparse and it's competitive.
Unemployment is also high and there isn't much around in the town itself unless you want to work in a shop or care home. A lot of people travel outside for work, but the rail service isn't the best - over an hour to get to Brighton, and the best part of two hours to get to London.
It's a similar picture along the East Sussex coast, but Hastings/St Leonards is beyond doubt the worst. Bexhill is slightly better, but the problems with unemployment, schools etc still remain, and there are rough bits there too. Eastbourne has more going for it in terms of shops and facilities, but it also has its problems. If I were you and looking to move to the area, I would maybe pick one of the villages slightly inland?