The blessing and the curse of traveling someplace really interesting is that there is going to be more than you can reasonably see in the time you have, no matter how much time you have. We've experienced that in spades during this trip, and creates a strange sort of tension that can ruin a good vacation.
As visitors from what is also (technically) a city, we have the urge to match that pace, and to EAT/SEE/DO EVERYTHING, and it's awesome. But at some point you realize that you can't swim with the shark, and even the women in black leggings and black sweaters smoking thin black cigarettes eventually go back to their tiny apartments at some point and just crash, because no one can keep up that pace without ill-advised quantities of Class III drugs. And we don't have thin cigarettes, nor the desire for a drug habit, and the coffee in New York is either overpriced or just awful, which is why it was inevitable that we'd end up pushing ourselves so hard that our feet felt like we had bruised the bones, and we just wanted to curl up and crash. You've gotta pace yourself if you're gonna get out alive, but pacing yourself means that there are going to be things you just.. miss. There's not enough time, but people back home will say things like "you didn't go to MOMA? WHY NOT?!?", and you'll start to feel like maybe that lazy breakfast you ate one morning while reading the paper and resting your feet was a huge waste of time.
We survive NYC somehow, and fly to London, our feet still sore and our energy levels still a bit off their prime. Thankfully, London is not New York. It is slower, more comfortable in its skin, more willing to pause for a breath now and then. However London soon reveals its own trap for the "do all the things" crowd: from the perspective of an American, London is old, just mind-numbingly old, and as a result every four steps there's some building or park or spot on the sidewalk that is incredibly historically significant. Those things you've heard or read or seen? Yeah, they all came from London, just down the street there, and if you'll just walk a mile this way, you can see the exact building where it was created. And so we walk, and walk, and walk, because what sort of twat doesn't go visit the site of Shakespeare's rise to fame? Or the home of ancient royalty? Or the graveyard full of famous people? Or the exact spot the Magna Carta was written? Because when you go home, people will ask "did you see the Crown Jewels? WHY NOT?!?" and you'll start to feel like maybe that afternoon you spent doing laundry and hanging out in the common room of the hostel resting your feet was a huge waste of time. And of course, this being London, the spot where you were sitting was where The Clash sat when they stood trial in this same room in 1978, and the hostel itself is the courthouse where Charles Dickens worked while writing Olive Twist. See? You can't swing a dead cat without hitting some history in London, and if you check it a second time, the cat's probably the former house cat of Richard III.
At some point you have to take a deep breath and realize that you can't see it all, you can't eat everything that is good, you can't experience everything. You'll go home, and before the plane even takes off you'll start remembering the things you didn't see, and you'll have to be comfortable with that being okay. The alternative is to push too hard, to drive yourself (and whoever might be traveling with you) too far, and to still not see it all. That quest was doomed from the start, and there's nothing you can do to change its fate.
Breathe. Breathe. Enjoy the moments of not doing anything significant or important or marked with a star in the guidebook. Those are the moments that might turn into something magical, like talking about Thai cooking with the family running the tiny, cheap Thai restaurant you hid in to escape the rush of the city, or discovering an all-but-abandoned train station and exploring it at your leisure, giving a confident smile to the maintenance crew and then ducking out a few seconds before they decide to ask you what the hell you're doing there. When you get home, you'll find that you can't really point to that moment in the travel guide, you can't describe it with sufficient fidelity to make your friends understand the magic of it. It's my assertion though that those unexpected adventures are the best reason to travel. Those unanticipated experiences will make you feel like sure, you might have missed going to MOMA, but no one will ever get to recapture that singular, unique moment you had. And when you think back on those moments, none of it will feel like a waste of time.