Can't beleive there are so many fellow Hastings-ers around here!
I have grown up in Hastings and in nearby villages and would thoroughly recommend it. Yes, it does has have some social deprivation problems but if you are currently in an area of London with problems as well (as I am now) then it is no worse in Hastings. Plus you don't have the same gang issues, and get to be by the seaside!
I agree that the biggest issue is schools. Like others - I would avoid Hollington like the plague - I know numerous teachers in the local primaries in the Hastings and Rother area, so am fairly up-to-date with the schools situation. Churchwood is another that I would try to avoid, it may have a decent ofsted but I certainly wouldn't send a child there. I would probably not pay too much attention to the ofsteds tbh, I would much rather focus on the feel of the schools when you look round. I know not everyone agrees, but I tend to think that for primary school, it is the home life that is far more important to the child - I went to a deprived school in the area and did not suffer in the slightest. The school managed to sort of stretch me and my parents did the rest; but I learnt a lot of other lessons there, I may well get flamed for this but I don't necessarily think that going to a school in a middle class enclave is always the best thing for a child. However, secondary schools are the main issue in the area.
It's a shame you don't drive as agree with others that the village schools are generally a lot nicer, have you tried looking at Battle? It has a fairly decent (but large) primary school but you get the massive advantage of Claverham for secondary. It is by far (imo) the best non-religious secondary in the area, one of the best in E.Sussex I would say. Prices are higher than Hastings though, especially as it is on the the train line.
As someone above said, three local schools (Filsham Valley, the Grove and Hillcrest) have now merged to become two academies instead, this has only just started, so results are not yet available. I think it will probably improve things, but they are improving what is currently a fairly dire situation so it still may not be great. However, if you have young children then it may be that in a few years time things will be much better. Certainly at the moment there would be no way I would send a child to any of those three schools - would home educate instead (as my parents had planned to do if my school had not worked out!) The final thing is the potential to use the Kent grammar system. Some of the grammar schools have a number of out of catchment places, or some operate a super-grammar system with no catchment - I am unsure of the current admissions criteria having sat the 11+ ten years ago. It is a very long day if you send your child to a school in Tunbridge Wells or Tonbridge (I got the train at 07:15 and returned at 17:00 if I had no clubs) but I got a fantastic education that I could never have got otherwise - as we could not have afforded to live in West Kent. Lots of children from the Hastings area attend these grammar schools for 6th form, as the Hastings schools don't have sixth forms, there are only sixth form colleges, which are another good for some and not for others, depending on maturity etc.
Sorry for the mammoth post, if you have any more questions about specific primaries I will try to answer them for you, but I encourage you to move to Hastings! I love it, it will always be my 'home' even though I no longer live there. Yes it has its problems but it also has a beautiful old town, the West Hill is fabulous, you can go to the beach and swim in the sea, fly kites up on the cliffs, it has the railway on the cliff, three crazy golfs, as well as beautiful rural countryside nearby. What's not to like?!