The distances port directly - Next to (same square or next square), Near (up to 6 squares away), Far (beyond that).
The abilities that interact with grid - here you would need to introduce some level and damage dependent rules:
monster damage works well for an area effect/distance effect function (mooks don't get to push you as far as a boss could)
add a modifier for a size (a mook elephant of huge size and an Black Fang Cadre mook are probably equal in terms of distance based effects)
We have off and on used a gridded matrix. Mostly it comes down to buy-in on what the different area abstractions mean in terms of real distances, defining what it means to "pop free" on a grid (we treat it as a disengage with a 5 foot step), and deciding if you want your area effects to effect a whole area or if you want them to still have the die roll for the number of enemies effected and just assume anyone else in the area is unaffected.
In general what we'd do is take whatever 4e had for similar effects and use them when it came to ranges and areas. The biggest shift is the minon rules - I might suggest just using the 4e ones over the 13th age ones since the 13th age minions IME fit a narrative frame better than a tactical one.