London/Paris

Could you fly home Sunday? With the time difference you get back home the same day. This would make your plan less tight, with 6 full days instead of 5, adding the extra day to Paris.
If it's not possible... Maybe your daughter has a preference between Paris and London? In which case, pick one.

It’s doable but if another day was added on either side of arrival and departure dates would help.

I Understand the short flight from NYC is a benefit and curtails some jet lag but with so much to see you do need time to allow mind and body to adjust.

Not to mention who knows what your arrival Heathrow experience will be like and depending on your accommodation choice you’ll need to factor in time to get there, unpack, etc.

Pre book must sees in both cities. I’m a big advocate of a first timer enjoying theatre in London. Have her review what’s scheduled to be on during your dates and if it’s a popular play consider pre Booking directly from the Theatre’s website.

Or you can always take time to see what’s available via the 1/2 price ticket booth. Not the major shows unless like Phantom they’ve been playing for years. Now available to review on line but you still have to go in person to pick them up.
https://officiallondontheatre.com/tkts/

If you can’t add a day or two. Pack lightly and hit the ground running. Have a daily plan. Helps if you double check opening and closing times of the sites, especially on Sundays.

She’s going to love this trip. Bravo

What a wonderful idea!! It is a rush rush trip, but she will get a taste of both cities. Just make sure you plan ahead to make the most out of your time.
It would be ideal if you could add a few days, but I understand that's not possible. Anyway, you can rest on the plane and on the train from Paris to London.

Honestly? With just 5 full days, I'd probably pick one or the other. Since you've been before you know there is plenty to keep you busy for 5 days in either location.

IF your daughter has her heart set on seeing highlights of both, then by all means do it. You've got knowledge of both cities so you can edit down to what sights might be most important/fun for her.

If you are returning to work on Monday, I'd fly home on Saturday as well.

She’s 19 — she will thrive on the pace of your trip while absorbing all she experiences! Have a great time!

I think returning on Saturday is a smart idea given she will either have classes or work on Monday and it’s better to have Sunday to handle the jet lag. You too! 😊

The young typically favor quantity over quality (they can say, I've been to Paris AND London, instead of just one, haha!). I'd shoot for both, and whet her appetite for when she can return independently in the future.

I spent 4 days in London and 5 in Paris on my first trip a couple years ago and I saw pretty much all the “standard stuff”. And I did that with my elderly father so we were usually done for the day about 5 or so except for dinner. Only one night did we do much and that was a bus tour. So both cities can be done in the time you have.

So, I would suggest doing both cities, but try to pick a hotel that is close to transportation and VERY close to the main locations you want to see. You can not afford to be spending an hour extra traveling in and out. If you think about it you spend on average 16 hours a day awake, lose two for eating. And an additional hour for misc plus an hour or so for washing up and such. So you are down to at max 12 hours of site seeing per day. An hour each way for 5 days is 10 hours. So basically saving a half hour each way is like adding a half day extra to the trip.

I would also advise taking a VERY late train to Paris (or are you going the other way...?). As late as reasonable so that you get to you hotel and promptly go to bed. This way you are traveling when you otherwise would not be doing much.

As for my logic about doing both. If you daughter likes to travel then she has a good chance of going back to Europe some day. At which point she can see whatever you did not get to in this trip. However odds are good that this could be the one and only time she is in Europe with her parents (unless you travel a lot as a family but it didn’t sound like it, at least not to Europe). So as she grows older she will have this trip to look back on and remember when she was in Europe with you.

In the mean time, she may not be as thrilled traveling with the rants. (As my nieces and nephews and sadly now GREAT nieces and nephews would say) but trust me she will brag about it to her friends all the time. I remember my first trip to Europe my older brother and sister (late teens at the time) were constantly complaining but to this day if they are out of hearing range of my father they still talk fondly of the trip.

Please note this kind of trip is NOT the more typical RS trip and thus is not usually what most folks on this forum are in favor of. As most on her tend to the less touristy locations and tend for slower more in depth trips.

My advice is to hit the highlights of the trip. Try and go to the shorter time requirement locations. Think the Eiffel Tower and the Arc de Triumph vs the Louvre and Versailles. To better maximize your time.

Try and get fast pass or reservations so you can skip the lines (we did this for a tour of the mechanical area of the Eiffel Tower and we skipped the line almost completely thus even with the tour we were up in the tower sooner then if we had stood in the normal security line for time entrance).
Stay in as close as possible.
Be willing to trade money for time if at all possible (closer hotels tend to be more expensive but save a lot of time)
Avoid the tourist busses for transportation (at least in London) as they take a LOT of time. In London and Paris often the River or the Subway is faster, and if going a shorter distance sometimes a cab as it goes directly and does not have to follow a route,
Take a lot of photos of the three of you (or at least your daughter and one of you at a time) as these are the photos that will grow more precious with time. And these are the photos she will look back at.

And please feel free to ask more questions as your planning advances.

If you get stuck trying to figure it out let me know and I will dig out my agenda for my. First trip, it worked pretty well. And if you dropped a couple things it would probably fit your trip.