I moved to Hinckley about 12 years ago and there are certainly worse places to live.
I would probably avoid Barwell and Earl Shilton as secondary schools especially poor and generally on the rougher side, however if you’re used to inner city poverty it’s fine. Burbage is basically a suburb of Hinckley but still retains bit of a village feel, however excellent motorway links push up house prices. Nuneaton can be good value but sociodemographically can be quite variable with patches of severe deprivation while in truth Hinckley mostly middle class homeowners.
Primary schools are all similar quality and I would have no qualms about my kids going to any, as a pp said though some years are quite full, the LEA will find you a place. About 4 years ago they moved from a middle school system to traditional primary secondary split so secondaries still finding their feet, in the long run I suspect Hastings and St Martins will be most desirable, Hastings selecting via house price and St Martins by religion.
There is an adequate local bus service around the town and 2 buses, trains an hour to Leicester. It’s fairly flat so walking not too taxing. Connections to the outlining villages poor by public transport though. Don’t discount proximity of Coventry, all the born and bred forget about it because it’s Warwickshire but it has as much culturally as Leicester and just as close, and IMO better employment opportunities.
Hinckley has all the amenities you would expect of a mid sized English town. Cinema, theatre, leisure centre, parks, markets, typically stagnating town centre, all 4 big supermarkets have a branch and new Lidl and Aldi both due to open shortly. Not much of a nightlife mind.
You probably need to come up for the a weekend to have a look around, but PM me if you have anything specific you want to ask.