I moved here from London just over 6 years. Never once regretted it. It's a brilliant place. I still work in London and the commute is fine and just as quick as places much closer to London - the season ticket is astronomical though but balanced by cheaper mortgages. Property isn't cheap in comparison to other places in Leicestershire but much cheaper than London obviously.
I wouldn't say there are any "bad" parts of MH tbh. Great Bowden is gorgeous and where I'm moving too when my numbers come up - village feel but stuck onto Harborough. You'll pay a bonkers premium for it though. There are some lovely villages nearby - The Langtons (Tur, Thorpe, East, West and Church!) but possibly a bit too rural for you.
Do you need to be able to get to London? If so, I can't think of anywhere else in Leicestershire that's so handy to be able to do so. Other than far west Leics where you could get the train from Rugby, Tamworth or Nuneaton. But it's much prettier this side! It's also really easy to get to Leicester or Nottingham too.
All the primary schools are good. And something like 95% of people get into their first choice - nothing like the London scrum for places.
The town centre is nice - quite a few independents and plenty of supermarkets (Waitrose, Aldi, Lidl and Sainsburys all close to each other). Nice pubs (a couple not very nice!), plenty of places to eat, lots of things to do for kids.
I love it (not a sponsored post by Harborough council I promise!!)