London transportation

Buy an Oyster card and fill it as needed at machines in Underground stations. Use it to pay for buses and the wonderful Underground, avoiding traffic as you travel the city. It is not a pass rather a method of accepted payment for bus and underground.
Get your tickets ahead for Windsor Castle, Tower of London, Westminster Abbey and Buckingham Palace( if it's open while you're there. We visited it in August, a wonderful experience)When we arrived at Windsor with our tickets already bought online, the lines stretched down the hill from the castle into the town. We went right up tp the top , at the castle and had a short wait. There was no wait at St. Paul's when we went there. Consider the Churchill War Rooms, buy tickets ahead online here as well as lines went way down the block. We skipped Kensington Palace.
You can do one ride on the hop on hop off bus but to really move around use your Oyster card.

I'll second the Oyster pass - I always get one and if there is money left on it, you can use it on your next trip to London.
I took my 80+ yr old Mom on the Hop on Hop off bus and she loved it. The only other place she wanted to go was Harrods (LOL) so we hopped in a traditional London Taxi to go there.
Happy Travels.

I’ve sent you a personal message about the Heathrow Express, the Oyster Card and the Paddington neighborhood.

Have a wonderful stay.

The Oyster Card is easy to buy, easy to use, and you can return the card at the airport at a machine and get back any unused funds plus the $5 fee for the card. The London transit system is amazing and its so easy to get around the city!! Uber is also inexpensive, and cabs are readily available at most train stations and hotels-they do take credit cards as well as cash.

Happy Travels✨💫

Personally, I think the HOHO buses are a waste of time and money. I would get to know the bus and tube system and use the Oyster card intended for tourists.

I would also purchase a SIM card for your phone so you can use it for directions. The Transport For London (www.tfl.gov) is a wonderful resource to planning trips while on the go. It provides you step by step getting from point A to B using buses and the tube.

Good luck and have fun.

A handy fact: if you think the seven-day travelcard is your best bet for transportation in London, buy a regular Oyster Card, not the Visitors Oyster Card. The Visitors Card will not take the seven- day pass. Second, follow Rick’s advice and try out the city buses. The next stop comes up on the info board in the bus, and is audibly announced as well. Third, I highly recommend that you avoid using the Central Line on the Underground, especially during rush hour, unless you just have to. Our experience is that the Central Line has significant delays much more than any other line. (Londoners will say the Northern Line is also rather problematic. I have not used the Northern Line enough to have an opinion either way.). Right now, the St. Paul’s station is compromised by escalator work, and it is much more efficient to take one of several buses running between St. Paul’s and Holborn. The Crossrail project’s Elizabeth Line, when it becomes operational, should relieve this, but completion of Crossrail has been pushed back at least until Fall 2019 (it was supposed to be done late this year, so who knows when it will actually be ready.). By the way, a much nicer approach to St Paul’s is walking up Bow Lane from Mansion House station on the District and Circle Lines. You get the added bonus of St. Mary le Bow church, a Christopher Wren church, whose bells are the test of whether or not one is a true Cockney.

Last September, I took my 94 year old expat mom there. She has returned many times over her lifetime, most recently 12 years ago and this one was surely to be her last. We arrived in the early morning hours and got into London by 11 am. While my husband and I have been there many times to visit our son who has lived there for 9 years, this trip was strictly for mom, planned with her wants/needs and desires in mind. London has changed so much since the last time she was there so we spent our first afternoon on the Afternoon Tea Bus London Tour. This was the perfect activity for the day we arrived. She says it was 'just what the doctor ordered'. Good luck and have a wonderful time.

try to see as many attractions as possible,

if you just want to see the attractions from outside, then the HOHO bus is fine. But if you want to actually visit the attractions and you know which attractions you want, then tube and buses are best.

The HOHO bus is excellent for giving an overview of a new city and help you find attractions to visit, but it is not the most time efficient way to visit them.

https://tfl.gov.uk/

Here is the comprehensive government guide to public transit in London. It includes an interactive trip planner. The regular Oyster can be purchased once you arrive. Note that there is a limit on the daily charges after which you ride for free. It's all explained on this link.
You can also use Google Maps, which provides similar route planning plus suggestions for pubs, restaurants etc.

I'm thinking they visited already since it was posted in April and the OP mentioned Summer trip with his wife.

yes, it was woken up by a self confessed leprechaun

But I am grateful, because I have a Visitor Oyster Card and may want to buy a weekly travel card next year. I didn't realize I won't be able to load the travel card onto my V.O.C.

I think the confusion is that the Oyster Card can be really two things. The card is just a fare vehicle. It can be both a prepaid card with a prepaid limit, and/or a travel card with additions depending on the zones you travel in. The travel card is something you buy for a whole week and put on to your Oyster Card as an electronic way to swipe in and out . The Travel Card is not metered. You travel as much as you want with in the zone limit you have bought in to for that week. And you get discounts on other services like the river boats. The NON-TRAVEL CARD, Oyster Card is a pre-paid, debit transportation card, sort of, since it maxes out at 6.30 pounds or so a day, and then doesn't charge any more to the debit of that day. Its stupidly complicated, yet it some how works. Renewing a Travel Card - on to an Oyster Card, retains any pre-load of fares. They are very much working in tandem, even if they seem like two different systems.