When you say near the high street, you mean Whetstone high road? The tube is called Totteridge and Whetstone but they're actually two distinct areas, Totteridge village is much, much posher with multi-squillion pound houses and the Orange Tree pub which is a posh gastro pub but very little in the way of useful everyday shops (assume the people that live there have staff to take care of the boring stuff like buying pints of milk 
), Whetstone is where the tube is and is more of a normal high road style area with all the regular stuff you'd expect in sururban north London like supermarkets and chemists and charity shops.
Whetstone assuming you do mean there is a perfectly nice area, if anything perhaps a shade nicer/posher than North Finchley or Finchley Central although they do all pretty much blend into one another. Whetstone has both a Waitrose and an M&S for instance which is my barometer of poshness anyway . The Griffin is a lovely casual family friendly pub with a huge beer garden and some other quite nice restaurants on the high road too. Let's be honest, it's deep suburb territory so nothing wildly exciting going on, none of the areas you mention have the wine bar and artisanal coffee shop feel of a Hamsptead or Highgate or even the hipster/shabby chic vibe of an East Finchley or a Walthamstow, but you have very nice green spaces (Darlands Nature reserve, Brook Farm park), there's a tennis club, a golf club, a swimming club/pool and a cricket club if you like sports, and you are pretty well placed to walk or get on the bus to any of High Barnet (more shops and restaurants, the hospital and the everyman cinema), East Barnet (more shops), North Finchley (more shops plus Art Depot theatre and arts complex) or the Finchley lido (bowling, cinema, chain restaurants). There's loads and loads of families in the area so the infrastructure for kids is pretty solid, all the clubs you'd expect etc.
Schools wise, the state primary schools in that part of Barnet are generally good with some excellent/outstanding ones, catchments can be a little tricky/narrow though so do check Ofsted (although don't be a slave to ratings) and the council website to understand admissions boundaries if a particular school is important to you. Secondary-wise you'll be in catchment for some of the excellent grammar schools but they really are very competitive to get into with a bit of a hot-house culture, the comprehensives can be more of a mixed bag, Finchley Catholic and St Michael's for instance are very good schools but obviously potentially not for you if you're not Catholic. Some of the others can be a bit rough although it's all relative really. And that would be no different if you were a mile or so down the road in Finchley itself TBH.