Yes, the stations you are using should have elevators or escalators, though they may not be convenient. I would doubt that you'll save time via subway, and it'll certainly be less convenient, but you'll save money. Taxi is a flat $30 + tolls + tip.

You'll want to use the stop at 51st/Lexington which is 1-2 blocks from your destination; or the 53rd/Lexington stop (they're both connected) which is 3-4 blocks away. However, to get off at 51st/Lex you'd have to make two transfers: the transfer to 4/5 as Ocean1971 mentions, and a second transfer to the 6. You're probably better off making a transfer at West 4th St. to the V (one level down by stairs/elevator), or an easier cross-platform transfer to the slightly-less-direct E at W 4th, 14th, 34th, or 42nd.