Lots of good riding from there -- if that's a consideration in your move, I wouldn't let availability of good cycling routes stop you. Most of my routes from center city go northwest through Haverford/the Main Line. Here's a good example: https://www.strava.com/routes/4273154

In Haverford, you are extremely close to the SRT (Schuylkill River Trail), which will take you all the way into the city or west past Valley Forge. There is no car traffic on the trail ^^; The area is pretty well off being near Villanova, so the roads are well maintained. Besides a couple main roads in town, traffic is fairly light and will get more sparse the further west you travel.

That looks like an awesome route with some great climbs. I live less than a mile from part of the route and am embarrassed to say I've ridden little of it. I need to dig into more of your routes.

I'll echo that there some great riding here and in general the roads are good and plenty of riders around so cars are (in general) better than average. I see a fair number of group rides on the weekends (usually when out running).

SRT is nice to get away from cars, but it's pretty flat and can be very crowded on nice weekend days, but in the mornings it is sparse and a great place to tuck into the bars without fear of cars (and it matches the elevation profile of most tri courses).

You can also keep heading southwest and once you get out to the West Chester/Kennett Square area you can ride forever in gorgeous rolling country.

I must have terrible timing b/c I frequently find vehicular traffic on the SRT. Township type trucks, an older guy on something like a motorized tricycle, and kids on a dirt bike - they HAD to have hit 30 mph. Bizarre, but true.

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Check out Strava and Garmin Connect heatmaps. Then "drill down" on segments, and see the routes people did when they rode them.

Also, there are a bunch of FB groups for local cycling and tri clubs, with links to ride announcements, etc.
Check out Southeast PA Cycling United, for starters.

(When you find Goshen Rd, in Malvern, besides the great rolling climbs, there is Rocky Run Alpaca Farm near it, and i'd like to think the alpacas are smiling at us, when we ride past...)

The SRT is flat, and depending on the time of year, can be great (weekday AMs), or crowded AF after 9a (on wkdns), or snow-covered, etc.

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I am fairly certain that I have literally never failed to see this guy when I ride the SRT. No matter what time of day/year

Lots of great riding heading out away from Philly. You can head up toward Evansburg St Park then out toward Harleysville etc, you can head toward Green Lane Reservoir, or out toward French Creek. Plenty you can do out the door, more if you drive to/from a starting point.

My sister lives in the main line. TBH, I like the riding options there more than the running.