Hi, Rachael - welcome to Boston! I lived there for several years before recently moving to Toronto. I used to work in Kendall Square at the Broad Institute, and I lived in an apartment in the Porter Square and Union Square areas of Somerville. I'd echo much of what has been said - ahall, acjospe, coach, Becks, and Cristina all have good advice.
For outdoor spaces - trail runs and training maps, I strongly recommend the Middlesex Fells in Medford. The
Skyline trail (white blazes) is one of my favorite trails; at 12 km with ~300m of climb, it's perfect for good training and catharsis. There are also numerous stroller-friendly trails.
This
google map has NEOC venues. North of the river, Middlesex Fells, Breakheart Reservation, Lynn Woods, and Prospect Hill all have pretty good maps, good terrain, and are large enough for diversity. The Blue Hills is also a great place, though it's harder to get to from Cambridge. Within ~90 minutes driving of the city, the best maps are Pawtuckaway in New Hampshire (<3), Baldwin Hill in Ashburnham, High Rock in Foxborough, and Mt. Tom and Earl's Trails in Northampton. There is a national event at Mt. Tom in April 2018.
I found biking into Cambridge from Somerville to be the best way to travel and mitigate the traffic, though as acjospe said, biking in Boston can be challenging. Google maps (among other places) has maps of some of the better
bike routes. I personally only used it infrequently, but you might also consider neighborhoods along the
commuter rail, as they might make living near good outdoor terrains (e.g. W. Medford) more feasible.
Finally, I lived several years without a car and with a car. Boston (and the US) has an hourly car share called Zipcar, and renting can be feasible. I suspect with 2 kids, it would be much more realistic to own a car. Almost all neighborhoods in Boston have good burrito options, though Cambridge especially so.
In any case, good luck! The Blue Hills Traverse, an annual mass-start 13 km orienteering race, is likely on Sunday November 19.
Maps near Cambridge (ask acjospe or some other Boston folks if you want actual maps):
Middlesex Fells, Medford - it's not quite as green as this might suggest, and very runnable in mid-Fall to mid-Spring
Breakheart, Saugus
Lynn Woods, Lynn - technical and dense vegetation, especially in the summer
Prospect Hill, Waltham, good hill, ideal for 4-6 km of orienteering
Pawtuckaway, and
west side - sex terrain in southern New Hampshire.
Contour only. Majestic.