I don't expect Google Maps Bike option to pick the the best route. It'll pick the shortest, and avoid some highways. So it's good for estimating distances, but not really for routing.

I normally draw my own routes on ridewithgps.com. I can route onto secondary roads, and if it looks too steep, undo and try a different road. Here's an example: Sunflower 100k ride. Hovering over the red elevation chart shows the grade at that point. Dragging a section of the climb shows it's statistics on the Metrics tab on the right. Lots of good info for a bike rider.

Strava Heat Map Here's the Pittsburgh area Heat Map
This is 18 months of rides recorded on strava.com, with the most commonly ridden roads in red, less common in blue. As you zoom in, it colors in more roads. You can bookmark any view, since the URL changes as you zoom and pan. I like the "gray" map style instead of the "blue" or "yellow".

Some roads are just an annoying but quick way out of town, but are still heavily ridden. But most red roads are where riders like to go ride. Strava started out as a performance rider or racer site. But now it has all kinds of riders, so the ride recordings are of all type of rides, from local casual rides to big hill climbing routes.

But locally, I see some steep climbs with lots of activity. Most "typical" riders probably avoid these most of the time. So the data may still be oriented to stronger riders.

I've been using this to browse other cities to see where I might think about riding. And I look at what roads are much less traveled compared to adjacent roads--it's probably good to avoid these if possible.


Strava Route Builder Link (You likely need a free membership to use this.)
This new Strava mapper is really impressing me with it's smart routing. It uses the Strava Heat Map data to pick the route, and it's been mostly very good to excellent when testing on local areas that I ride.

It allows clicking and dragging a point on the route line to a new waypoint. It'll recalculate the route to include that point within a second or two.

I click the Settings icon, then turn on "Global Heatmap" to see what other nearby roads are also popular, to see if I have some good alternative roads I could use.

I usually start by just clicking the starting location and the end point, if it's within a few hundred miles. Then I get an idea of the mileage and elevations. Next, I usually want to reroute at least part of the route.

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Testing Strava's routing:
I wondered how it would do on rural routes with less bike traffic. It's still picking good routes.
For example: Harrison Ohio to Brookville Indiana. The main highway, US52, looks good on paper, but it's extremely annoying to ride, busy with enough curves that traffic can't easily pass the riders. Our club rides always avoid it if possible.

Google Maps follows busy US52 all the way. 17.7 miles. Nope.
EDIT-- Oct 2016: now google maps takes a somewhat better route, avoiding half of the US52 highway. It's interesting that they've changed their routing methods for bikes!
EDIT--Dec 2016: it's now showing the direct, annoying route, and an alternative hillier route.
EDIT--Aug 2017: only the bad US52 route is showing. But if I move the starting location slightly, it now also shows that slightly better Oct 2016 alternative route. Come on, Google, you can do better.
Google Map link.

Strava
Strava is using the side roads that I've been on with club rides. Mostly lower traffic. Two big climbs, instead of following the river valley on US52. It even routes on the (potholed) road along the opposite side of the river from US52. We like to take that hidden road--it's rough, but very scenic and quiet. 21.8 miles. I'd ride this!
Harrison to Brookville, using popularity

I clicked "minimize elevation" and it rerouted. 22.7 miles. Another good route, and it went quite far out of the way to avoid hills. I'd perhaps cross a couple of the smaller creek valleys to shorten the ride.
Harrison to Brookville, popularity and minimized elevation


Strava's Pittsburgh to Millersburg route
Here's the default Strava route: Map Link. It swings way north, and takes lots of side roads. It crosses the Ohio even farther northeast than East Liverpool, at Monaca / Beaver.

You'll probably want a mapping computer like a Garmin to navigate it! I've never exported a Strava map, I'll have to try it sometime.

That's probably too far to make an optimal route. Click Edit on the finished map, then click and drag a spot on the route line to a new position. Yeah, that's really helpful on these long distance routes.

On the Heat Map, there's a lot more riding activity along the Ohio River, downstream from Pittsburgh. And more activity near population centers in NW Ohio than the rural hills directly between Pittburgh and Millersburg. That must influence which route is selected. But the more direct route shows rider activity as you zoom in, and could make a very nice bike route.


EDIT-- Strava Route Builder sometimes uses gravel roads or bike trails. And it's routed up some steeper hills where there's a short detour to avoid the climb. But it's usually picking good roads.
EDIT--it now has an option to show the Heat Map as you make your route. I always turn this option on--it's on the left side, click the Settings icon. It's very nice to see popular roads when I'm considering if I want to reroute the strava selected route.

You'll probably want to upload the route to a GPS device. Strava routes usually have a lot of turns!