I'd second the Fallen Leaf campground. There are fun little trails between the campground and the lake you could play around on, and it is a very pretty area.
The climb from Spooner Lake to Marlett Lake is a grind; not technically challenging, just steep at altitude. I did the Flume last summer. Mostly it is not tough, but you do have to watch the trail and not the scenery. The fire road descent back to the lake (Tahoe) needs to be handled with some caution. My friend and I rode the shuttle back; it was about $12 and a nice amenity.
I don't know about current conditions, but for fun easy rides, I'd check out Paige Meadows above Sunnyside at the north shore. It's a beautiful area, a series of linked meadows connected by a trail network. If you are ambitious, you can do a loop from there to Alpine Meadows, then back to Tahoe City via the Truckee River bike path