Silver Lakes area in the buckhorn is a great place, but as has been mentioned, the trails are heavily used. Get familiar enough with the area where you're very comfortable going off trail and over ridges and thru draws. (Google earth study time, and print paper maps, or bring a good mapped gps. Both, actually... batteries die, no cell service. That can make you comfortable the first run.) Beautiful area for high buck or archery.
Can get very rugged when you're trekking off on your own, so be aware.
Good initial plan since you live close by, but like was also mentioned, why not doing during season (also) with your tags and gear?!?!