I would focus one day on Lake Placid and one day on Wilmington, even though you could ride trails in both areas on the same day as they are only 9 miles apart.
Pull up a BETA trail map online when you read this and it should make pretty good sense:
www.betatrails.org
Lake Placid: Start out on Loggers/Lussi system from one of the trailheads surrounding the LPC golfcourse. Work your way through this system in a variety of ways as you chose, and eventually to the jackrabbit trail which connects it to the Craigwood system. Over at Craigwood is more flow trail style, while Lussi/Loggers more technical.
Wilmington: Must do All In at Hardy Road trails. 45 mins or so climb to a view of Whiteface and a sweet downhill with 2-3 route options. Several other trails are part of that Hardy system, which are also fun, but All In is the most bang for buck in terms of sustained downhill.
Quaker Mt trail is shorter, but very fun intermediate more flowy trail that connects downtown Wilmington to the Hardy Rd trails. You could actually park over near there then use Quaker to access Hardy and reverse back to town and your car.
Flume system is more of the original trail system in Wilmington, but has had some really fun new trails added. Check out Gulo Gulo which connects to PMD (see below) and then the Ridge trail is super technical, with trails of various levels mixed in throughout the system. Avoid Marble Mt. trail, unless you want to have to hike a bike or just love extra super rocky shit more than me, you may think you're on a hiking trail if you get lost and end up here. Eventually it ties into Ridge trail.
PMD - poor mans downhill...3 mile shuttleable downhill from the road that leads to the Whiteface Toll Rd. booth. Well mapped on BETA trails. You can also pedal up it if you want from the trailhead/exit behind Up a Creek restaurant in Wilmington on Rt. 86. Definitely shuttle this once at least, its super fast and fun.
Best thing is to stop in and buy BETA trail map at one of the local bike shops. Placid Planet has them and I think High Peaks Cyclery does too.
Also town of Wilmington runs a shuttle on certain Sundays for $5 all day for poor mans downhill. Not sure of dates this year you'd need to look that up or contact BETA.