Thanks very much for the replies thus far.
To clarify, I would like to purchase a house with a yard, and access to transit in to the city (train or bus), no more than 50 mins commute (god help me), but I don't necessarily need walking access to that station.
Again, I wouldn't ask you what you make. And if you're not comfortable disclosing price range for a house, that's understandable; but the answers are going to be more vague. The single most important question I'd have before I even gave a well thought-out answer is this: Do you have kids? And do you plan to? Because the quality of the public school can vary. Of course, there are always privates, parochials and charters, but the privates are obscenely expensive and the parochials may not interest everybody and the charters are often not available.
Montclair might offer the best of all worlds, ie , say about 37-40 minutes into the city, six train stops, good schools, fantastic downtown, tons of folks moving from the city for the exact same reason. Maplewood has a smaller downtown, but is nearby. If you're conservative, might not be the town for you, since both are very liberal, Maplewood exceptionally so. Both have obnoxiously-high taxes, though. I know about seven or eight people between the two towns and only one pays less than $15,000 in taxes. He pays $13,500.
I second the Ridgewood suggestion. Great schools, nice downtown, safe, houses seem to hold their value (and rebounded back faster than many other towns, like mine lol), train. Costly, although the taxes might be a shade cheaper than Montclair because you're not supporting Newark.
Paramus has similar priced homes to those, but the taxes are absurdly low in comparison because of all the ratables. All the malls/stores keep the taxes way down. But there is no downtown, traffic is a bitch on Saturday and no train to speak of, although there are plenty of buses, and you're right off 17 & 4 to drive in.
West Orange, South Orange, Westwood, Glen Rock are all nice. As is Edgewater, although yards are harder to find there.
Teaneck, Englewood, Hoboken, Weehawkin, Jersey City (some sections like Newport) all have great qualities, although (if you have kids) their public schools have all faced various degrees of questions, and yards will be a lot harder to come by in all but Teaneck & Englewood. I see that was a strong preference for you.
Hope some of this helped.