This is a great resource to search different places for their accessibility there in the UK.
So if there's a specific theatre or museum or anything you're wondering about visiting, you could look it up for the review and information. Their Twitter feed is good too.
This gives some helpful bus hints:
and this too:
I've found Google Maps was great when I was plotting my bus adventures when I lived and worked there for 2 months. Click the public transportation bus icon at the top of the directions screen, and it makes it easy.
I'm in pain most of the time while traveling (scoliosis was severe as a kid, metal rod in back, collagen damage/pain) and the buses were WAY better and easier than the Tube for me. I also have double vision from eye operation, with the escallators being twice as fast and twice as steep in the Tube, I wanted to avoid them. Plus I find no logic to the idea of traveling in a dark tunnel when I can see and explore the city on a bus. The only tricky part was looking at the top of the bus stop, to see specifically which stop it was, and to match that stop's letter to the route map. if they were crowded, it was easy to wait 10 min for the next one. The rest was just about connecting the routes and counting the number of stops so I'd be ready to get off when I needed to. :)
And these kinds of trips with your 87 yr old Dad are massively valuable in your long-term pile o' memories, Go for the hotel you WANT by Tower Bridge !!!! (my 2 pence. :) Night time view could be great photo ops. Valuable stuff.
I also found that Travelodge.co.uk has many options at good prices, have stayed in the Southwark one not too far from the Tower Bridge (not visible tho) and also the one in Windsor. They have accessible rooms with showers (not tubs) that were good. They were basic, but clean, good breakfasts, twin beds were too narrow, but otherwise good. I've stayed in Premier Inn too, the beds were better in those but the service and location was better with Travelodge. That one in City Hall building with Premier Inn can be comfy, but that side of Waterloo station has a constant stream of people, it will be at least somewhat noisy (tho I did read somewhere that they were getting their windows soundproofed, don't know how much that helps when you may need window open sometimes). The bus stops at Waterloo are only on the hotel side going one way out, then they are on the whole other side of Waterloo station coming in. Transport for London's web site's great for bus plotting too, of course. Google maps can show you which stop is near your hotel, when you zoom in on the street map, then that info is helpful on tfl's site.
It can be very helpful for your airport travels to request a wheelchair for your Dad if he's willing to give it a try. It can zoom you through lots of the lines :) Usually the only requirement is to have some difficulty navigating the whole airport without one. I overheard a stewardess saying that if anyone requests one, they HAVE to give it to them, no questions asked. I used to work for a wheelchair company, so I know people have varying opinions about them. In the case of airports, they can be a great help, though.
Have a great time! Do whatever is the most fun for you guys. :)