Squilchuck Road to Mission Ridge Road and then the Liberty Beehive USFS 9712 Road up to Beehive Reservoir is a good one for an afternoon drive. You can keep going all the way to Haney Meadows and the old mining town of Liberty or out Swauk Meadows onto US97 for a day trip. The trail between Haney Meadow and Beehive isn’t technical, but there is a washed out/ heavily rutted spot crossing a scree field on the side of a ridge you need to be aware of. You’ll know the spot when you see the parts and pieces of plastic fenders and bumpers off of low clearance passenger cars scattered on the side of the slope.
Another good shorter day trip is take US 2 to 97 and then Old Blewett Pass Highway at Peshastin Creek. It was the original road over the mountains, so it is paved, narrow with lots of potholes and a few rock falls. There’s FS roads branching off the summit to explore, again nothing technical. The old highway comes out back onto US 97 at Swauk Creek.
You can make a big loop by going up 97 to Entiat and taking Entiat River Road to Mad River Road, stop for lunch at Coopers General Store in Ardenvoir, then take Tillicum USFS 5800 all the way up to French Corral and then the 5200 up to Sugarloaf Fire Lookout. Back down to French Corral and then drop down Van Creek 7520 to Eagle Creek Road and then on into Leavenworth for dinner. Keeping in mind that around a quarter of FS roads are passable to passenger vehicles you have a lot of basic trail choices within an easy drive from Wenatchee. The Washington Backroads Discovery Route runs through Wenatchee. The few trails I’ve thrown out here barely scratches the surface of what’s available locally.
My advice is get a decent map app. I use Gaia GPS and Trails Offroad, there are others. Also the PNW-NF app is handy.