Well, the Whites are awesome. If you like being above tree-line, and you've tired of the Whites, you'll have to head out west. I'm personally very fond of the Sangre de Christo Range in Colorado, but I like a lot of the trails near Aspen and Maroon Bells as well. Just about any of the Colorado 14ers are nice...even Pikes Peak.
If you want to stick to the Northeast, try the Adirondacks. Only a few of the peaks have the same feeling you get in the Whites, but the hikes are all great. Giant Mtn has some great rock formations and big slabs. Whiteface is a great hike..except for the ski lift. Marcy can be crowded on weekends..but the ridgeline to the Wolfjaws is a great part of that trail.
Mt. Mansfield and Camel's Hump in VT are excellent hikes. I like Camel's Hump a bit more....no ski trails on the mountain!
Mt. Monondonk in southern NH is also a good hike. Really nice views. It's in NH but not part of the Whites.
Pick up the following book:
"High Peaks of the Northeast" by Bruce Scofield. I use it a lot. (It just happens to be on my desk.) It's great for basic planning, but get more detailed maps from USGS, the Forest Service, or the hiking clubs.
Also:
The Adirondack Mountain Club's Guide to the High Peaks:
http://www.adk.org
The Long Trail Guide or Day Hiking Guide from the Green Mountain Club:
http://www.greenmountainclub.org
There are numerous books on Colorado. I have one simply titled: "Colorado Fourteeners." It got a lot of use back when I worked out west. It's in a box now somewhere otherwise I'd give you the author.