You can reach the base of the Nose with no real talus.
Whitehorse Slab has, what, a minute, plus walking up the driveway, maybe 3 total? And Cathedral's not much more. Parts of Rumney are about the same, though steeper. CP Slab is a contender certainly vs the epic Poke-O approach of 10 minutes or more.
Compared with these, Lost City is almost as remote a wilderness destination as Ragged Mountain, in terms of approach time.