Any tips/ideas for first day in London after red-eye?

That sounds great. I'd add a stop at a grocery store to check out British cookies etc for the room.

Sounds like a good plan. I would suggest only planning on things that don't require advance tickets. If you end up having travel irregular operations, you don't want to be on the hook for timed tickets that first day. I might just switch the eye (if it requires advance tickets) for a Thames boat ride.

The area near Waterloo Station is one of my favorite areas to stay in while in London. I will suggest avoiding the hop on hop off bus at any time during your trip.

When my husband and I arrive on a red eye to Europe, we often go on a Sandesman "free tour" for an overview of the city. I have seen many recommendations for London Walks on this website but I can't comment on it since I personally haven't used their services. The Sandman tours are pay what you feel the tour is worth. London Walks charges a set fee.

My daughters (14 and 18) and I had fun walking around St. James' Park. I think your plan is very good though.

It depends on how you handle jet lag. We always take a nap between 1-3 or 2-4. Either way no more two hours and back to one of the parks for outdoor activity or light snack. But stay in the sun. I would avoid the Eye. It will lull you to sleep. Like being in a rocking chair.

I think the Sky garden has better views than the London eye. It’s also free so saves you some £. Free tickets are released on every Mondays 3 weeks in advance.

https://skygarden.london/booking/

People handle jet lag differently, for me the Eye would be a good choice because it's interesting, close to the hotel, full of daylight, and gives you a nice overview of the city you'll be visiting. However, the tickets are timed. Tickets may be available on the spot, but probably with a long line, which would be a bad idea after a long flight. And you can't count on good weather for high-level viewing. Walking the south bank would be a good idea, though -- or any of the parks.

What would lull me to sleep is a boat ride (and I love boat rides) or a HOHO bus.

I have used London Walks in London and in Paris and I really enjoyed them. Their guides are very well versed in their particular walk. You just check their listing for available walks and show up and pay the guide before the start of the walk. As others have mentioned the Sky Garden would be a better option that the Eye as the weather could not be conducive to a good view. Enjoy your time in London. And yes your first day you want to keep moving and plan to go to bed a little earlier than your normal.

I would go to your hotel, either check in early or drop off your luggage until check-in, then just walk around and look at some of the sights the first day. There is a lot to see in that area. did that many years ago after an early morning arrival in London (and will do the same next spring when I arrive at 7:30 am).

One thing you might do is find someplace to eat breakfast after you get there. I just posted an article that said one way to reduce jet lag is to eat a hearty breakfast once you arrive your destination. This was based on a study by Northwestern Univ. and Santa Fe Ins. That will kill some time, and then I would just get out and walk around.

ETA: This post about a walk Roger Ebert used to take might give you some ideas. https://community.ricksteves.com/travel-forum/books-movies/the-perfect-london-walk

Thank you so much everyone! Appreciate the feedback. Good to hear we are on the right track. Regarding the eye versus Sky garden. Researched that already. The Eye is a 5 minute walk and the garden is about 30. Plus, I am traveling with a 10 year old! She will enjoy the Eye way more.

Go on the Eye by all means but don’t prebook. If the weather on the day is bad it will be a big disappointment.
I can’t agree with taking an afternoon nap. People react to jet lag in different ways and maybe it works for some but taking a nap to me just encourages your body to stay more on your home time zone than the new one. The sooner you get used to UK time the quicker you will get the energy to enjoy over here. Your original plan to be out in the fresh air walking is an excellent one.

You can disagree with the idea of an afternoon nap but ours is based on our experience. We use to gut it out with staying awake till evening. Had some very miserable dinners as we tried to stay awake and then were wide awake at 4 am but still tired. We find the nap recharges our batteries just enough to get through a nice, evening meal, and retire around 10 to 11 pm. For us the nap works so don't knock it until you have tried it.

Your plan sounds ideal. Allows senses to adjust and helps to stretch legs after a long flight. I always take the redeye LAX to LHR and after immigration, using public transport and checking in I head out to explore my neighborhood. I’ll locate closest Boots, a coffee spot, pub and market. I buy shortbread cookies and a large bottled water.

For my late lunch/ early dinner I stop at a pub before the after work patrons arrive. Nice dinner, pleasant stroll back to my accommodation. Will admit that I might take Advil PM to insure a deep sleep.

Up early and the adventure begins.

Mine is also based on experience Frank. Over the years I have taken countless flights across the Atlantic and also flights to places 5-8 hours ahead of the UK. Fair enough if a nap works for you but I made a few errors when I first started travelling, enough for me to give up the practice a long time ago.. Like you, though, I can only advise on my personal experience.