I think I can help you out with that, the answer that fits 'very very tall' in the New York Times crossword is likely 'lofty'. However, another possibility could be 'skyhigh' or even 'statuesque', but I'm leaning more towards 'lofty' as it's a pretty common term used to describe something that's extremely tall, and it's a word that's often used in crosswords, so it might just be the one you're looking for.