I used to live there and still visit family and friends there regularly. It's not Muswell Hill.... but it's creeping closer and closer as MH becomes so expensive and there is trickle down effect to Alexandra Park, Bounds Green and ultimately PG.
It definitely does still feel like London – not suburban (others may disagree but to me, suburban means 1930s houses eg Southgate and Oakwood) - It has no tube though, but a train line into Finsbury Pk and Moorgate and very regular buses up Green Lanes to Wood Green (Piccadilly line). Or head to Southgate tube, depending where in PG you end up.
The Lakes Estate, squashed between Fox Lane and Aldermans Hill / Broomfield Park are lovely characterful houses, many now split into flats. Some really nice cafés (Starfish, and the one near to the station whose name I can't remember) and a very posh bakery (Holtwhite's) face on to the park. Broomfield Park is lovely and has a very active friends group, an orchard, wetlands, playing fields and a community cafe.
The other side of Fox Lane - Burford Gardens, Cranley Gardens etc - are smaller houses and slightly less desirable but still a very solid address - and then if you cross over Bourne Hill, there are more roads that run perpendicular to Green Lanes and Hoppers Rd, all the way up to Winchmore Hill – some really nice characterful houses around here.
I personally prefer west side of Green Lanes to the other side, although I think there are some quite nice properties down e.g. Lightcliffe Road and thereabouts. As others have said, it all gets less desirable the closer you get to the A406 and the A10. Edmonton is to be avoided.
Hazelwood Lane Primary School is okay I think, if schools are of important to you, a big multicultural London primary - but the local secondary school (Broomfield) is pretty bad; consider looking at Winchmore School catchment instead if you have soon-to be-teenagers.
I think there's quite a burgeoning sense of local community as people move there, wanting to be in Muswell Hill in their hearts, but the desire for a house with a garden winning the day.
Good luck with your search!