I can't help trying to fit your parameters into my back yard, so heare goes:
West to East (a totally arbitrary decision) -- Start at Route 113 (Holderness Rd). Morgan Tr - Crawford Ridgepole Tr - Sandwich Notch Rd - Algonquin Tr - Bennett St Tr - Flat Mtn Pond Tr - McCrillis Tr - Rollins Tr - Dicey's Mill Tr - Walden Tr - Lawrence Tr - Old Paugus Tr - Beeline - Piper Tr - Middle Sister Tr - Carter Ledge Tr - Nickerson Ledge Tr - Piper Tr.
It's only 40 miles, but 10 miles/day on this route will be a good workout. Mountain Summits include Morgan, Percival, Squam, Doubletop, Sandwich, Whiteface, Passaconaway, Nanamocomuck, (Wonalancet) Hedgehog, Paugus, Chocorua, Three Sisters. It includes an end-to-end traverse of the Sandwich Range Wilderness, a remote high pond, some river walking and 13,200' of climbing (avaerage 3400'/day).
OK, so it's not flatlandish. But you're not going to find 50 miles of flatlandish hiking in the Whites